### Bibliography

[1]
:
A determination of all associative algebras in two, three and four units over a nonmodular field __\( \frak{F} \)__.
M.S. Thesis,
University of Chicago,
1927.
phdthesis

[2] : Algebras and their radicals and division algebras. Ph.D. thesis, University of Chicago, 1928. Advised by L. E. Dickson. MR 2611246 phdthesis

[3] : “Normal division algebras satisfying mild assumptions,” Proc. Nat. Acad. Sci. U.S.A. 14 : 12 (December 1928), pp. 904–906. JFM 54.0161.04 article

[4] : “The group of the rank equation of any normal division algebra,” Proc. Natl. Acad. Sci. USA 14 : 12 (December 1928), pp. 906–907. JFM 54.0161.05 article

[5] :
“A determination of all normal division algebras in sixteen units,”
Bull. Am. Math. Soc.
34 : 4
(1928),
pp. 410–411.
Abstract only; paper in *Trans. Am. Math. Soc.* **31**:2 (1929).
JFM
54.0166.16
article

[6] :
“On the structure of normal division algebras,”
Ann. Math. (2)
30 : 1–4
(1928–1929),
pp. 322–338.
An abstract was published in *Bull. Am. Math. Soc.* **35**:2 (1929).
MR
1502886
JFM
55.0682.01
article

[7] :
“Normal division algebras in __\( 4p^2 \)__ units, __\( p \)__ an odd prime,”
Ann. Math. (2)
30 : 1–4
(1928–1929),
pp. 583–590.
MR
1502907
JFM
55.0683.01
article

[8] : “The structure of any algebra which is a direct product of rational generalized quaternion division algebras,” Ann. Math. (2) 30 : 1–4 (1928–1929), pp. 621–625. MR 1502911 JFM 55.0683.02 article

[9] : “On the rank equation of any normal division algebra,” Bull. Am. Math. Soc. 35 : 3 (1929), pp. 335–338. MR 1561740 JFM 55.0090.03 article

[10] :
“A determination of all normal division algebras in sixteen units,”
Trans. Am. Math. Soc.
31 : 2
(1929),
pp. 253–260.
An abstract was published in *Bull. Am. Math. Soc.* **34**:4 (1928).
MR
1501481
JFM
55.0090.04
article

[11] :
“The rank function of any simple algebra,”
Proc. Natl. Acad. Sci. U.S.A.
15 : 4
(April 1929),
pp. 372–376.
An abstract was published in *Bull. Am. Math. Soc.* **35**:4 (1929).
JFM
55.0683.03
article

[12] :
“On the structure of normal division algebras,”
Bull. Am. Math. Soc.
35 : 2
(1929),
pp. 182–183.
Abstract only; paper in *Ann. Math.* **30**:1–4 (1928–1929).
JFM
55.0092.03
article

[13] :
“The rank function of any simple algebra,”
Bull. Am. Math. Soc.
35 : 4
(1929),
pp. 441.
Abstract only; paper in *Proc. Natl. Acad. Sci. U.S.A.* **15**:4 (1929).
JFM
55.0092.05
article

[14] :
“A necessary and sufficient condition for the non-equivalence of any two rational generalized quaternion division algebras,”
Bull. Am. Math. Soc.
36 : 8
(1930),
pp. 535–540.
An abstract was published in *Bull. Am. Math. Soc.* **36**:3 (1930).
MR
1561990
JFM
56.0145.03
article

[15] :
“A construction of all non-commutative rational division algebras of order eight,”
Bull. Am. Math. Soc.
36
(1930),
pp. 214.
Article only; paper in *Ann. Math.* **31**:4 (1930).
JFM
56.0152.24
article

[16] :
“New results in the theory of normal division algebras,”
Trans. Am. Math. Soc.
32 : 2
(1930),
pp. 171–195.
An abstract was published in *Bull. Am. Math. Soc.* **36**:3 (1930).
MR
1501532
JFM
56.0146.01
article

[17] :
“A determination of the integers of all cubic fields,”
Ann. Math. (2)
31 : 4
(October 1930),
pp. 550–566.
An abstract was published in *Bull. Am. Math. Soc.* **36**:3 (1930).
MR
1502961
JFM
56.0870.01
article

[18] : “A note on an important theorem on normal division algebras,” Bull. Am. Math. Soc. 36 : 10 (1930), pp. 649–650. MR 1562029 JFM 56.0145.04 article

[19] :
“Determination of all normal division algebras in thirty-six units of type __\( R_2 \)__,”
Am. J. Math.
52 : 2
(1930),
pp. 283–292.
MR
1507918
JFM
56.0145.06
article

[20] :
“The non-existence of pure Riemann matrices with normal multiplication algebras of order sixteen,”
Ann. Math. (2)
31 : 3
(1930),
pp. 375–380.
An abstract was published in *Bull. Am. Math. Soc.* **36**:3 (1930).
MR
1502951
JFM
56.0869.02
article

[21] : “The integers of normal quartic fields,” Ann. Math. (2) 31 : 3 (July 1930), pp. 381–418. MR 1502952 JFM 56.0870.02 article

[22] : “On the structure of pure Riemann matrices with non-commutative multiplication algebras,” Proc. Natl. Acad. Sci. U.S.A. 16 : 4 (April 1930), pp. 308–312. JFM 56.0329.08 article

[23] :
“New results in the theory of normal division algebras,”
Bull. Am. Math. Soc.
36
(1930),
pp. 198–199.
Abstract only; paper in *Trans. Am. Math. Soc.* **32**:2 (1930).
JFM
56.0152.19
article

[24] :
“On direct products, cyclic division algebras, and pure Riemann matrices,”
Proc. Natl. Acad. Sci. U.S.A.
16 : 4
(April 1930),
pp. 313–315.
See also *Trans. Am. Math. Soc.* **33**: 1 (1931).
JFM
56.0869.01
article

[25] :
“On the Wedderburn norm condition for cyclic algebras,”
Bull. Am. Math. Soc.
36 : 11
(1930),
pp. 804.
Abstract only; paper in *Bull. Am. Math. Soc.* **37**:4 (1931).
JFM
56.0153.01
article

[26] :
“A necessary and sufficient condition for the non-equivalence of any two rational generalized quaternion division algebras,”
Bull. Am. Math. Soc.
36 : 3
(1930),
pp. 213.
Abstract only; paper in *Bull. Am. Math. Soc.* **36**:8 (1930).
JFM
56.0152.23
article

[27] :
“A determination of the integers of all cubic fields,”
Bull. Am. Math. Soc.
36 : 3
(1930),
pp. 199.
Abstract only; paper in *Ann. Math.* **31**:4 (1930).
JFM
56.0152.22
article

[28] :
“The non-existence of pure Riemann matrices with normal multiplication algebras of order sixteen,”
Bull. Am. Math. Soc.
36 : 3
(1930),
pp. 199.
Abstract only; paper in *Ann. Math.* **31**:3 (1930).
JFM
56.0152.20
article

[29] :
“Division algebras over an algebraic field,”
Bull. Am. Math. Soc.
37 : 10
(1931),
pp. 777–784.
An abstract was published in *Bull. Am. Math. Soc.* **37**:7 (1931).
MR
1562255
JFM
57.0161.01
Zbl
0003.05303
article

[30] :
“Errata: ‘On direct products, cyclic division algebras, and pure Riemann matrices’,”
Trans. Am. Math. Soc.
33 : 4
(October 1931),
pp. 999.
Errata for paper published in *Trans. Am. Math. Soc.* **33**:1 (1931).
MR
1500511
article

[31] : “The structure of matrices with any normal division algebra of multiplications,” Ann. Math. (2) 32 : 1 (January 1931), pp. 131–148. MR 1502987 JFM 57.0162.01 Zbl 0001.26603 article

[32] :
“A note on cyclic algebras of order sixteen,”
Bull. Am. Math. Soc.
37 : 10
(1931),
pp. 727–730.
An abstract was published in *Bull. Am. Math. Soc.* **37**:7 (1931).
MR
1562244
JFM
57.0160.03
Zbl
0003.05302
article

[33] :
“On direct products, cyclic division algebras, and pure Riemann matrices,”
Trans. Am. Math. Soc.
33 : 1
(1931),
pp. 219–234.
Errata published in *Trans. Am. Math. Soc.* **33**:4 (1931). See also *Proc. Natl. Acad. Sci. U.S.A.* **16**:4 (1930).
MR
1501586
JFM
57.0158.03
Zbl
0001.11602
article

[34] :
“On normal division algebras of type __\( R \)__ in thirty-six units,”
Trans. Am. Math. Soc.
33 : 1
(January 1931),
pp. 235–243.
MR
1501587
JFM
57.0160.01
Zbl
0001.11701
article

[35] :
“On the Wedderburn norm condition for cyclic algebras,”
Bull. Am. Math. Soc.
37 : 4
(1931),
pp. 301–312.
An abstract was published in *Bull. Am. Math. Soc.* **36**:11 (1930).
MR
1562142
JFM
57.0160.02
Zbl
0001.26701
article

[36] :
“On direct products,”
Trans. Am. Math. Soc.
33 : 3
(1931),
pp. 690–711.
An abstract was published in *Bull. Am. Math. Soc.* **37**:5 (1931).
MR
1501610
JFM
57.0159.01
Zbl
0002.24605
article

[37] :
“Normal division algebras of order __\( 2^{2^m} \)__,”
Proc. Natl. Acad. Sci. USA
17 : 6
(June 1931),
pp. 389–392.
JFM
57.0161.02
Zbl
0002.11502
article

[38] : “The structure of pure Riemann matrices with non-commutative multiplication algebras,” Rend. Circ. Mat. Palermo 55 : 1 (1931), pp. 57–115. JFM 57.0161.03 Zbl 0001.26602 article

[39] :
“A note on cyclic algebras of order sixteen,”
Bull. Am. Math. Soc.
37 : 7
(1931),
pp. 527–528.
Abstract only; paper in *Bull. Am. Math. Soc.* **37**:10 (1931).
JFM
57.0172.01
article

[40] :
“On the construction of cyclic algebras with a given exponent,”
Bull. Am. Math. Soc.
37 : 7
(1931),
pp. 528.
Abstract only; paper in *Am. J. Math.* **54**:1 (1932).
JFM
57.0172.02
article

[41] :
“The integers represented by sets of positive ternary quadratic forms,”
Bull. Am. Math. Soc.
37 : 3
(1931),
pp. 169.
Abstract only; paper in *Am. J. Math.* **55**:1–4 (1933).
JFM
57.0199.08
article

[42] :
“On direct products,”
Bull. Am. Math. Soc.
37 : 5
(1931),
pp. 355.
Abstract only; paper in *Trans. Am. Math. Soc.* **33**:3 (1931).
JFM
57.0171.22
article

[43] :
“Division algebras over an algebraic field,”
Bull. Am. Math. Soc.
37 : 7
(1931),
pp. 528.
Abstract only; paper in *Bull. Am. Math. Soc.* **37**:10 (1931).
JFM
57.0172.03
article

[44] :
“Algebras of degree __\( 2^e \)__ and pure Riemann matrices,”
Ann. Math. (2)
33 : 2
(April 1932),
pp. 311–318.
MR
1503054
JFM
58.0143.02
Zbl
0004.10001
article

[45] : “Normal division algebras of degree four over an algebraic field,” Trans. Am. Math. Soc. 34 : 2 (1932), pp. 363–372. MR 1501642 JFM 58.0144.01 Zbl 0004.10002 article

[46] :
“On normal simple algebras,”
Trans. Am. Math. Soc.
34 : 3
(1932),
pp. 620–625.
An abstract was published in *Bull. Am. Math. Soc.* **38**:3.
MR
1501653
JFM
58.1026.04
Zbl
0005.05002
article

[47] :
“On the construction of cyclic algebras with a given exponent,”
Am. J. Math.
54 : 1
(1932),
pp. 1–13.
An abstract was published in *Bull. Am. Math. Soc.* **37**:7 (1931).
MR
1506868
JFM
58.0141.05
Zbl
0003.24405
article

[48] :
“A determination of all normal division algebras over an algebraic number field,”
Trans. Am. Math. Soc.
34 : 3
(1932),
pp. 722–726.
An abstract was published in *Bull. Am. Math. Soc.* **38**:3 (1932).
MR
1501659
Zbl
0005.05003
article

[49] :
“A construction of non-cyclic normal division algebras,”
Bull. Am. Math. Soc.
38 : 6
(1932),
pp. 449–456.
An abstract was published in *Bull. Am. Math. Soc.* **38**:3 (1932).
MR
1562415
JFM
58.0143.01
Zbl
0005.00603
article

[50] :
“A note on normal division algebras of order sixteen,”
Bull. Am. Math. Soc.
38 : 10
(1932),
pp. 703–706.
An abstract was published in *Bull. Am. Math. Soc.* **38**:7 (1932).
MR
1562492
JFM
58.0141.03
Zbl
0005.34202
article

[51] :
“A note on normal division algebras of order sixteen,”
Bull. Am. Math. Soc.
38 : 7
(1932),
pp. 496.
Abstract only; paper in *Bull. Am. Math. Soc.* **38**:10 (1932).
JFM
58.0153.05
article

[52] :
“On normal simple algebras,”
Bull. Am. Math. Soc.
38 : 3
(1932),
pp. 179–180.
Abstract only; paper in *Trans. Am. Math. Soc.* **34**:3 (1932).
JFM
58.0153.01
article

[53] :
“A determination of all normal division algebras over an algebraic number field,”
Bull. Am. Math. Soc.
38 : 3
(1932),
pp. 179.
Abstract only; paper in *Trans. Am. Math. Soc.* **34**:3 (1932).
JFM
58.0153.02
article

[54] :
“A construction of non-cyclic normal division algebras,”
Bull. Am. Math. Soc.
38 : 3
(1932),
pp. 180–181.
Abstract only; paper in *Bull. Am. Math. Soc.* **38**:6 (1932).
JFM
58.0153.03
article

[55] :
“The integers represented by sets of ternary quadratic forms,”
Am. J. Math.
55 : 1–4
(1933),
pp. 274–292.
An abstract was published in *Bull. Am. Math. Soc.* **37**:3 (1931).
MR
1506964
JFM
59.0181.03
Zbl
0006.29004
article

[56] :
“Normal division algebras over algebraic number fields not of finite degree,”
Bull. Am. Math. Soc.
39 : 10
(1933),
pp. 746–749.
An abstract was published in *Bull. Am. Math. Soc.* **39**:9 (1933).
MR
1562722
JFM
59.0159.02
Zbl
0008.00104
article

[57] :
“Cyclic fields of degree eight,”
Trans. Am. Math. Soc.
35 : 4
(1933),
pp. 949–964.
An abstract was published in *Bull. Am. Math. Soc.* **39**:1 (1933).
MR
1501727
JFM
59.0158.03
Zbl
0008.00201
article

[58] : “A note on the Dickson theorem on universal ternaries,” Bull. Am. Math. Soc. 39 : 8 (1933), pp. 585–588. MR 1562680 JFM 59.0181.02 Zbl 0007.33704 article

[59] : “Non-cyclic algebras of degree and exponent four,” Trans. Am. Math. Soc. 35 : 1 (1933), pp. 112–121. MR 1501674 JFM 59.0158.02 Zbl 0006.15103 article

[60] : “On universal sets of positive ternary quadratic forms,” Ann. Math. (2) 34 : 4 (October 1933), pp. 875–878. MR 1503139 JFM 59.0181.04 Zbl 0007.39204 article

[61] :
“On primary normal division algebras of degree eight,”
Bull. Am. Math. Soc.
39 : 4
(1933),
pp. 265–272.
An abstract was published in *Bull. Am. Math. Soc.* **39**:1 (1933).
MR
1562597
JFM
59.0159.01
Zbl
0007.05503
article

[62] :
“A note on the equivalence of algebras of degree two,”
Bull. Am. Math. Soc.
39 : 4
(1933),
pp. 257–258.
An abstract was published in *Bull. Am. Math. Soc.* **39**:3 (1933).
MR
1562594
JFM
59.0158.04
Zbl
0007.05502
article

[63] :
“On certain imprimitive fields of degree __\( p^2 \)__ over __\( P \)__ of characteristic __\( p \)__,”
Bull. Am. Math. Soc.
39 : 11
(1933),
pp. 870.
Abstract only; paper in *Ann. Math.* **35**:2 (1934).
JFM
59.0168.20
article

[64] :
“On universal sets of positive ternary quadratic forms,”
Bull. Am. Math. Soc.
39 : 5
(1933),
pp. 345–346.
Abstract only; paper in *Ann. Math.* **34**:4 (1933).
JFM
59.0187.07
article

[65] :
“Integral domains of rational generalized quaternion algebra,”
Bull. Am. Math. Soc.
39 : 7
(1933),
pp. 501.
Abstract only; paper in *Bull. Am. Math. Soc.* **40**:2 (1934).
JFM
59.0168.18
article

[66] :
“Normal division algebras over a modular field,”
Bull. Am. Math. Soc.
39 : 11
(1933),
pp. 870–871.
Abstract only; paper in *Trans. Am. Math. Soc.* **36**:2 (1934).
JFM
59.0168.22
article

[67] :
“On primary normal division algebras of degree eight,”
Bull. Am. Math. Soc.
39 : 1
(1933),
pp. 41.
Abstract only; paper in *Bull. Am. Math. Soc.* **39**:4 (1933).
JFM
59.0168.15
article

[68] :
“Cyclic fields of degree eight,”
Bull. Am. Math. Soc.
39 : 1
(1933),
pp. 41.
Abstract only; paper in *Ann. Math.* **35**:4 (1933).
JFM
59.0168.16
article

[69] :
“A note on the equivalence of algebras of degree two,”
Bull. Am. Math. Soc.
39 : 3
(1933),
pp. 198–199.
Abstract only; paper in *Bull. Am. Math. Soc.* **39**:4 (1933).
JFM
59.0168.17
article

[70] :
“Normal division algebras over algebraic number fields not of finite degree,”
Bull. Am. Math. Soc.
39 : 9
(1933),
pp. 667.
Abstract only; paper in *Bull. Am. Math. Soc.* **39**:10 (1933).
JFM
59.0168.19
article

[71] :
“Cyclic fields of degree __\( p^n \)__ over __\( F \)__ of characteristic __\( p \)__,”
Bull. Am. Math. Soc.
40 : 8
(1934),
pp. 625–631.
An abstract was published in *Bull. Am. Math. Soc.* **40**:3 (1934).
MR
1562919
Zbl
0010.00402
article

[72] :
“Normal division algebras over a modular field,”
Trans. Am. Math. Soc.
36 : 2
(1934),
pp. 388–394.
An abstract was published in *Bull. Am. Math. Soc.* **39**:11 (1933).
MR
1501750
JFM
60.0105.02
Zbl
0009.19502
article

[73] :
“A solution of the principal problem in the theory of Riemann matrices,”
Ann. Math. (2)
35 : 3
(July 1934),
pp. 500–515.
An abstract was published in *Bull. Am. Math. Soc.* **40**:3.
MR
1503176
Zbl
0010.00401
article

[74] :
“Normal division algebras of degree 4 over __\( F \)__ of characteristic 2,”
Am. J. Math.
56 : 1–4
(1934),
pp. 75–86.
MR
1507931
JFM
60.0105.01
Zbl
0008.24202
article

[75] :
“Integral domains of rational generalized quaternion algebras,”
Bull. Am. Math. Soc.
40 : 2
(1934),
pp. 164–176.
An abstract was published in *Bull. Am. Math. Soc.* **39**:7 (1933).
MR
1562813
Zbl
0008.29301
article

[76] : “On normal Kummer fields over a non-modular field,” Trans. Am. Math. Soc. 36 : 4 (1934), pp. 885–892. MR 1501774 JFM 60.0915.03 Zbl 0010.14902 article

[77] :
“On certain imprimitive fields of degree __\( p^2 \)__ over __\( P \)__ of characteristic __\( p \)__,”
Ann. Math. (2)
35 : 2
(April 1934),
pp. 211–219.
An abstract was published in *Bull. Am. Math. Soc.* **39**:11 (1933).
MR
1503156
JFM
60.0915.02
Zbl
0009.24302
article

[78] :
“The principal matrices of a Riemann matrix,”
Bull. Am. Math. Soc.
40 : 12
(1934),
pp. 843–846.
An abstract was published in *Bull. Am. Math. Soc.* **40**:9 (1934).
MR
1562985
JFM
60.0908.01
Zbl
0010.29202
article

[79] : “On a certain algebra of quantum mechanics,” Ann. Math. (2) 35 : 1 (January 1934), pp. 65–73. MR 1503142 JFM 60.0902.03 Zbl 0008.42104 article

[80] : “On the construction of Riemann matrices. I,” Ann. Math. (2) 35 : 1 (January 1934), pp. 1–28. MR 1503140 JFM 60.0908.02 Zbl 0010.00304 article

[81] :
“Involutorial simple algebras and real Riemann matrices,”
Proc. Natl. Acad. Sci. U.S.A.
20 : 12
(1934),
pp. 676–681.
An abstract was published in *Bull. Am. Math. Soc.* **40**:11 (1934). See also *Ann. Math.* (2) **36**:4 (1935).
JFM
60.0909.01
Zbl
0010.29203
article

[82] :
“Cyclic fields of degree __\( p^n \)__ over __\( F \)__ of characteristic __\( p \)__,”
Bull. Am. Math. Soc.
40 : 3
(1934),
pp. 218.
Abstract only; paper in *Bull. Am. Math. Soc.* **40**:8 (1934).
JFM
60.0113.22
article

[83] :
“The principal matrices of a Riemann matrix,”
Bull. Am. Math. Soc.
40 : 9
(1934),
pp. 652.
Abstract only; article in *Bull. Am. Math. Soc.* **40**:12 (1934).
JFM
60.0059.05
article

[84] :
“A solution of the principal problem in the theory of Riemann matrices,”
Bull. Am. Math. Soc.
40 : 3
(1934),
pp. 217.
Abstract only; paper in *Ann. Math.* **35**:3 (1934).
JFM
60.0916.11
article

[85] :
“Involutorial simple algebras and real Riemann matrices,”
Bull. Am. Math. Soc.
40
(1934),
pp. 808.
Abstract only; paper in *Proc. Natl. Acad. Sci. U.S.A.* **20**:12 (1934).
JFM
60.0916.10
article

[86] : “On the construction of Riemann matrices. II,” Ann. Math. (2) 36 : 2 (April 1935), pp. 376–394. MR 1503230 JFM 61.1037.02 Zbl 0011.38904 article

[87] : “A note on the Poincaré theorem on impure Riemann matrices,” Ann. Math. (2) 36 : 1 (January 1935), pp. 151–156. MR 1503214 JFM 61.0124.01 Zbl 0011.00603 article

[88] : “On cyclic fields,” Trans. Am. Math. Soc. 37 : 3 (1935), pp. 454–462. MR 1501797 JFM 61.0124.02 Zbl 0011.29005 article

[89] :
“Involutorial simple algebras and real Riemann matrices,”
Ann. Math. (2)
36 : 4
(October 1935),
pp. 886–964.
See also *Proc. Natl. Acad. Sci. U.S.A.* **20**:12 (1934).
MR
1503260
JFM
61.1038.01
Zbl
0012.39102
article

[90] :
“Simple algebras of degree __\( p^e \)__ over a centrum of characteristic __\( p \)__,”
Bull. Am. Math. Soc.
41 : 7
(1935),
pp. 489.
Abstract only; paper in *Trans. Am. Math. Soc.* **40**:1 (1936).
JFM
61.0127.09
article

[91] :
“Normal division algebras of degree __\( p^e \)__ over __\( F \)__ of characteristic __\( p \)__,”
Trans. Am. Math. Soc.
39 : 1
(January 1936),
pp. 183–188.
MR
1501840
JFM
62.0101.01
Zbl
0013.10202
article

[92] :
“Simple algebras of degree __\( p^e \)__ over a centrum of characteristic __\( p \)__,”
Trans. Am. Math. Soc.
40 : 1
(July 1936),
pp. 112–126.
An abstract was published in *Bull. Am. Math. Soc.* **41**:7 (1935).
MR
1501866
JFM
62.0101.02
Zbl
0014.29102
article

[93] :
“Normalized integral bases of algebraic number fields, I,”
Bull. Am. Math. Soc.
42 : 11
(1936),
pp. 811.
Abstract only; paper in *Ann. Math.* **38**:4 (1937).
JFM
62.0172.06
article

[94] :
“__\( p \)__-algebras over a field generated by one indeterminate,”
Bull. Am. Math. Soc.
43 : 10
(1937),
pp. 733–736.
MR
1563627
JFM
63.0875.01
Zbl
0017.24501
article

[95] :
“Normalized integral bases of algebraic number fields. I,”
Ann. Math. (2)
38 : 4
(October 1937),
pp. 923–957.
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