A. Adrian Albert: collected mathematical papers 2 Nonassociative algebras and miscellany
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Format: | Buch |
Sprache: | Englisch |
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Providence, RI
American Math. Soc.
1993
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Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006756107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
Umfang: | LXXVII, 938 S. Ill. |
ISBN: | 0821800078 |
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adam_text | ARTICLES APPEARING
IN VOLUME
Part 1
Preface xvii
Bibliography xix
Professional Biography of A(braham) Adrian Albert xxxi
Ph.D. Students of A. Adrian Albert xxxvii
A. A. Albert by Daniel Zelinsky, Amer. Math. Monthly 80
no. 6, June July (1973), 661 665. xxxix
Abraham Adrian Albert, 1905 1972 by Nathan Jacobson,
Bull. Amer. Math. Soc. 80 (1974), 1075 1100. xlv
Abraham Adrian Albert, A biographical memoir by Irving
Kaplansky, Biographical Memoirs, National Academy of
Sciences 51 (1980), 3 22. lxv
A. Adrian Albert by Israel N. Herstein, Collection of articles
dedicated to the memory of Abraham Adrian Albert, Scripta
Math. 29, no. 3 4, (1973). lxxv
1. A determination of all normal division algebras in sixteen
units, Trans. Amer. Math. Soc. 31 (1929), 253 260. 1
2. On the rank equation of any normal division algebra,
Bull. Amer. Math. Soc. 35 (1929), 335 338. 9
A. ADRIAN ALBERT v
ARTICLES APPEARING IN VOLUME
3. The rank function of any simple algebra, Proc. Nat. Acad.
Sci. U.S.A. 15 (1929), 372 376. 13
4. On the structure of normal division algebras, Ann. of
Math. (2) 30 (1929), 322 338. 19
5. Normal division algebras in 4 p2 units, p an odd prime,
Ann. of Math. (2) 30 (1929), 583 590. 37
6. The structure of any algebra which is a direct product of
rational generalized quaternion division algebras, Ann. of
Math. (2) 30 (1929), 621 625. 45
7. The non existence of pure Riemann matrices with normal
multiplication algebras of order sixteen, Ann. of Math. (2)
31 (1930), 375 380. 51
8. A necessary and sufficient condition for the
non equivalence of any two rational generalized quaternion
division algebras, Bull. Amer. Math. Soc. 36 (1930),
535 540. 57
9. Determination of all normal division algebras in
thirty six units of type R2, Amer. J. Math. 52 (1930),
283 292. 63
10. A note on an important theorem on normal division
algebras, Bull. Amer. Math. Soc. 36 (1930), 649 650. 73
11. New results in the theory of normal division algebras,
Trans. Amer. Math. Soc. 32 (1930), 171 195. 75
12. A construction of all non commutative rational division
algebras of order eight, Ann. of Math. (2) 31 (1930),
567 576. 101
13. The structure of pure Riemann matrices with
non commutative multiplication algebras, Palermo
Rendiconti 55 (1931), 57 115. 111
14. On direct products, cyclic division algebras, and pure
Riemann matrices, Proc. Nat. Acad. Sci. U.S.A. 16(1930),
313 315. 171
vi COLLECTED MATHEMATICAL PAPERS
ARTICLES APPEARING IN VOLUME
15. On normal division algebras of type R in thirty six
units, Trans. Amer. Math. Soc. 33 (1931), 235 243. 175
16. On the Wedderburn norm condition for cyclic algebras,
Bull. Amer. Math. Soc. 37 (1931), 301 312. 185
17. A note on cyclic algebras of order sixteen, Bull. Amer.
Math. Soc. 37 (1931), 727 730. 197
18. On direct products, Trans. Amer. Math. Soc. 33 (1931),
690 711. 201
19. Division algebras over an algebraic field, Bull. Amer.
Math. Soc. 37 (1931), 777 784. 223
20. The structure of matrices with any normal division
algebra of multiplications, Ann. of Math. (2) 32 (1931),
131 148. 231
21. On the construction of cyclic algebras with a given
exponent, Amer. J. Math. 54 (1932), 1 13. 249
22. Algebras of degree 2e and pure Riemann matrices, Ann.
of Math. (2) 33(1932), 311 318. 263
23. A construction of non cyclic normal division algebras,
Bull. Amer. Math. Soc. 38 (1932), 449 456. 271
24. Normal division algebras of degree four over an
algebraic field, Trans. Amer. Math. Soc. 34 (1932), 363 372. 279
25. On normal simple algebras, Trans. Amer. Math. Soc. 34
(1932), 620 625. 289
26. A note on normal division algebras of order sixteen,
Bull. Amer. Math. Soc. 38 (1932), 703 706. 295
27. (with H. Hasse), A determination of all normal division
algebras over an algebraic number field, Trans. Amer. Math.
Soc. 34 (1932), 722 726. 299
28. A note on the equivalence of algebras of degree two,
Bull. Amer. Math. Soc. 39 (1933), 257 258. 305
A. ADRIAN ALBERT vii
ARTICLES APPEARING IN VOLUME
29. On primary normal division algebras of degree eight,
Bull. Amer. Math. Soc. 39 (1933), 265 272. 307
30. Non cyclic algebras of degree and exponent four, Trans.
Amer. Math. Soc. 35 (1933), 112 121. 315
31. Normal division algebras over algebraic number fields
not of finite degree, Bull. Amer. Math. Soc. 39 (1933),
746 749. 325
32. Cyclic fields of degree eight, Trans. Amer. Math. Soc. 35
(1933), 949 964. 329
33. On the construction of Riemann matrices I, Ann. of
Math. (2)35(1934), 1 28. 345
34. Normal division algebras of degree 4 over F of
characteristic 2, Amer. J. Math. 56 (1934), 75 86. 373
35. On certain imprimitive fields of degree p2 over P of
characteristic p, Ann. of Math. (2) 35 (1934), 211 219. 385
36. Normal division algebras over a modular field, Trans.
Amer. Math. Soc. 36 (1934), 388 394. 395
37. A solution of the principal problem in the theory of
Riemann matrices, Ann. of Math. (2) 35 (1934), 500 515. 403
38. Cyclic fields of degree p over F of characteristic p,
Bull. Amer. Math. Soc. 40 (1934), 625 631. 419
39. On normal Kummer fields over a non modular field,
Trans. Amer. Math. Soc. 36 (1934), 885 892. 427
40. The principal matrices of a Riemann matrix, Bull.
Amer. Math. Soc. 40 (1934), 843 846. 435
41. A note on the Poincare theorem on impure Riemann
matrices, Ann. of Math. (2) 36 (1935), 151 156. 439
42. On the construction of Riemann matrices II, Ann. of
Math. (2) 36 (1935), 376 394. 445
viii COLLECTED MATHEMATICAL PAPERS
ARTICLES APPEARING IN VOLUME
43. On cyclic fields, Trans. Amer. Math. Soc. 37 (1935),
454 462. 465
44. Involutorial simple algebras and real Riemann matrices,
Ann. of Math. 36 (1935), 886 964. 475
45. Normal division algebras of degree pe over F of
characteristic p, Trans. Amer. Math. Soc. 39 (1936),
183 188. 555
46. Simple algebras of degree pe over a centrum of
characteristic p, Trans. Amer. Math. Soc. 40 (1936),
112 126. 561
47. p algebras over a field generated by one indeterminate,
Bull. Amer. Math. Soc. 43 (1937), 733 736. 577
48. Non cyclic algebras with pure maximal subfields, Bull.
Amer. Math. Soc. 44 (1938), 576 579. 581
49. On cyclic algebras, Ann. of Math. (2) 39 (1938),
669 682. 585
50. A note on normal division algebras of prime degree,
Bull. Amer. Math. Soc. 44 (1938), 649 652. 599
51. On ordered algebras, Bull. Amer. Math. Soc. 46 (1940),
521. MR 1, 328. 603
52. On p adic fields and rational division algebras, Ann. of
Math. (2) 41 (1940), 674 693. MR 2, 123. 605
53. Division algebras over a function field, Duke Math. J. 8
(1941), 750 762. MR 3, 365. 625
54. Two element generation of a separable algebra, Bull.
Amer. Math. Soc. 50 (1944), 786 788. MR 6, 115. 639
55. Absolute valued real algebras, Ann. of Math. (2) 48
(1947), 495 501; Correction in Bull. Amer. Math. Soc. 55
(1949), 1191. MR 8, 561; 11, 76. 643
A. ADRIAN ALBERT ix
ARTICLES APPEARING IN VOLUME
56. Absolute valued algebraic algebras, Bull. Amer. Math.
Soc. 55 (1949), 763 768. MR 11, 76. 651
57. Leonard Eugene Dickson (1874 1954), Bull. Amer.
Math. Soc. 61 (1955), 331 345. MR 17, 2. 657
58. On involutorial algebras, Proc. Nat. Acad. Sci. U.S.A. 41
(1955), 480 482. MR 17, 9. 673
59. A property of ordered rings, Proc. Amer. Math. Soc. 8
(1957), 128 129. MR 18, 557. 677
60. On involutorial associative division algebras, Scripta
Math. 26 (1963), 309 316. MR 31, 3451. 679
61. A normal form for Riemann matrices, Canad. J. Math.
17(1965), 1025 1029. Mi? 32, 111. 687
62. New results on associative division algebras, /. Algebra 5
(1967), 110 132. MR 34, 2617. 693
63. On associative division algebras (Retiring Presidential
Address), Bull. Amer. Math. Soc. 74 (1968), 438 454. MR
36, 5166. 717
64. A note on certain cyclic algebras, /. Algebra 14 (1970),
70 72. MR 40, 4297. 735
65. Tensor products of quaternion algebras, Proc. Amer.
Math. Soc. 35 (1972), 65 66. MR 45, 6855. 739
Acknowledgments 741
x COLLECTED MATHEMATICAL PAPERS
ARTICLES APPEARING IN VOLUME
Part 2
Preface xvii
Bibliography xix
Professional Biography of A(braham) Adrian Albert xxxi
Ph.D. Students of A. Adrian Albert xxxvii
A. A. Albert by Daniel Zelinsky, Amer. Math. Monthly 80
no. 6, June July (1973), 661 665. xxxix
Abraham Adrian Albert, 1905 1972 by Nathan Jacobson,
Bull. Amer. Math. Soc. 80 (1974), 1075 1100. xlv
Abraham Adrian Albert, A biographical memoir by Irving
Kaplansky, Biographical Memoirs, National Academy of
Sciences 51 (1980), 3 22. lxv
A. Adrian Albert by Israel N. Herstein, Collection of articles
dedicated to the memory of Abraham Adrian Albert, Scripta
Math. 29, no. 3 4, (1973). lxxvii
1. The integers of normal quartic fields, Ann. of Math. (2)
31 (1930), 381 418. 1
2. A determination of the integers of all cubic fields, Ann.
of Math. (2) 31 (1930), 550 566. 39
3. The integers represented by sets of ternary quadratic
forms, Amer. J. Math. 55 (1933), 274 292. 57
A. ADRIAN ALBERT xi
ARTICLES APPEARING IN VOLUME
4. On universal sets of positive ternary quadratic forms,
Ann. of Math. (2) 34 (1933), 875 878. 77
5. A note on the Dickson theorem on universal ternaries,
Bull. Amer. Math. Soc. 39 (1933), 585 588. 81
6. On a certain algebra of quantum mechanics, Ann. of
Math. (2) 35 (1934), 65 73. 85
7. Integral domains of rational generalized quaternion
algebras, Bull. Amer. Math. Soc. 40 (1934), 164 176. 95
8. A note on matrices defining total real fields, Bull. Amer.
Math. Soc. 43 (1937), 242 244. 109
9. Normalized integral bases of algebraic number fields I,
Ann. of Math. (2) 38 (1937), 923 957. 113
10. A quadratic form problem in the calculus of variations,
Bull. Amer. Math. Soc. 44 (1938), 250 253. 149
11. Symmetric and alternate matrices in an arbitrary field, I,
Trans. Amer. Math. Soc. 43 (1938), 386 436. 153
12. Quadratic null forms over a function field, Ann. of
Math. (2) 39 (1938), 494 505. 205
13. A rule for computing the inverse of a matrix, Amer.
Math. Monthly 48 (1941), 198 199. MR 2, 243 217
14. Quadratic forms permitting composition, Ann. of Math.
(2)43(1942), 161 177. MR 3, 261. 219
15. Non associative algebras. I. Fundamental concepts and
isotopy, Ann. of Math. (2) 43 (1942), 685 707. MR 4, 186. 237
16. Non associative algebras. II. New simple algebras, Ann.
of Math. (2) 43 (1942), 708 723. MR 4, 186. 261
17. The radical of a non associative algebra, Bull. Amer.
Math. Soc. 48 (1942), 891 897. MR 4, 130. 277
xii COLLECTED MATHEMATICAL PAPERS
ARTICLES APPEARING IN VOLUME
18. An inductive proof of Descartes rule of signs, Amer.
Math. Monthly 50 (1943), 178 180. MR 4, 195. 285
19. Quasigroups. I, Trans. Amer. Math. Soc. 54 (1943),
507 519. MR 5, 229. 289
20. Algebras derived by non associative matrix
multiplication, Amer. J. Math. 66 (1944), 30 40. MR 5,
227. 303
21. The matrices of factor analysis, Proc. Nat. Acad. Sci.
U.S.A. 30 (1944), 90 95. MR 5, 209. 315
22. The minimum rank of a correlation matrix, Proc. Nat.
Acad. Sci. U.S.A. 30 (1944), 144 146. MR 6, 6. 321
23. Quasigroups. II, Trans. Amer. Math. Soc. 55 (1944),
401 419. MR 6, 42. 325
24. Quasiquaternion algebras, Ann. of Math. (2) 45 (1944),
623 638. MR 6, 115. 345
25. On Jordan algebras of linear transformations, Trans.
Amer. Math. Soc. 59 (1946), 524 555. MR 8, 63. 361
26. The Wedderburn principal theorem for Jordan algebras,
Ann. of Math. (2) 48 (1947), 1 7. MR 8, 435. 393
27. A structure theory for Jordan algebras, Ann. of Math.
(2) 48 (1947), 546 567. MR 9, 77. 401
28. On the power associativity of rings, Summa Brasil.
Math. 2 (1948), no. 2, 21 33. MR 10, 97. 423
29. Power associative rings, Trans. Amer. Math. Soc. 64
(1948), 552 593. MR 10, 349. 437
30. On right alternative algebras, Ann. of Math. (2) 50
(1949), 318 328. MR 10, 503. 479
31. A theory of trace admissible algebras, Proc. Nat. Acad.
Sci. U.S.A. 35 (1949), 317 322. MR 11, 6. 491
A. ADRIAN ALBERT xiii
ARTICLES APPEARING IN VOLUME
32. Almost alternative algebras, Portugal. Math. 8 (1949),
23 36. MR 11, 316. 497
33. A note on the exceptional Jordan algebra, Proc. Nat.
Acad. Sci. U.S.A. 36 (1950), 372 374. MR 12, 5. 511
34. A theory of power associative commutative algebras,
Trans. Amer. Math. Soc. 69 (1950), 503 527. MR 12, 475. 515
35. New simple power associative algebras, Summa Brasil.
Math. 2 (1951), 183 194. MR 14, 11. 541
36. Power associative algebras, Proc. Internat. Congress
Math. (Cambridge, Mass., (1950)), vol. 2, Amer. Math.
Soc, Providence, R.I., 1952, pp. 25 32. MR 13, 527. 553
37. On nonassociative division algebras, Trans. Amer.
Math. Soc. 72 (1952), 296 309. MR 13, 816. 561
38. On simple alternative rings, Canad. J. Math. 4 (1952),
129 135. 575
39. On commutative power associative algebras of degree
two, Trans. Amer. Math. Soc. 74 (1953), 323 343. MR 14,
614. 583
40. Rational normal matrices satisfying the incidence
equation, Proc. Amer. Math. Soc. 4 (1953), 554 559. MR
15,94. 605
41. The structure of right alternative algebras, Ann. of
Math. (2) 59 (1954), 408 417. MR 15, 774. 611
42. (with M. S. Frank), Simple Lie algebras of characteristic
p, Univ. ePolitec. Torino. Rend. Sem. Mat. 14(1954/55),
117 139. MR 18, 52. 621
43. On Hermitian operators over the Cayley algebra, Proc.
Nat. Acad. Sci. U.S.A. 41 (1955), 639 640. MR 17, 123. 645
44. A property of special Jordan algebras, Proc. Nat. Acad.
Sci. U.S.A. 42 (1956), 624 625. MR 18, 375. 647
xiv COLLECTED MATHEMATICAL PAPERS
ARTICLES APPEARING IN VOLUME
45. On certain trinomial equations in finite fields, Ann. of
Math. (2) 66 (1957), 170 178. MR 19, 394. 649
46. (with B. Muckenhoupt), On matrices of trace zero,
Michigan Math. J. 4 (1957), 1 3. MR 18, 786. 659
47. On partially stable algebras, Trans. Amer. Math. Soc.
84 (1957), 430 443. MR 19, 1156. 663
48. (with N. Jacobson), On reduced exceptional simple
Jordan algebras, Ann. of Math. (2) 66 (1957), 400 417.
MR 19, 527. 677
49. Addendum to the paper on partially stable algebras,
Trans. Amer. Math. Soc. 87 (1958), 57 62. MR 19, 1157. 695
50. A construction of exceptional Jordan division algebras,
Ann. of Math. (2) 67 (1958), 1 28. MR 19, 1036. 701
51. On the orthogonal equivalence of sets of real symmetric
matrices, /. Math. Mech. 7 (1958), 219 235. MR 19, 1153. 729
52. A solvable exceptional Jordan algebra, J. Math. Mech. 8
(1959), 331 337. MR 21, 681. 747
53. (with L. J. Paige), On a homomorphism property of
certain Jordan algebras, Trans. Amer. Math. Soc. 93
(1959), 20 29. MR 21, 7240. 755
54. (with John Thompson), Two element generation of the
projective unimodular group, Illinois J. Math. 3 (1959),
421 439. MR 21, 5681. 765
55. Finite noncommutative division algebras, Proc. Amer.
Math. Soc. 9 (1958), 928 932. MR 21, 1994. 785
56. Finite division algebras and finite planes, Proc. Sympos.
Appl. Math., Vol. 10, Amer. Math. Soc, Providence, R.I.
(I960), pp. 53 70. MR 22, 6831. 791
A. ADRIAN ALBERT xv
ARTICLES APPEARING IN VOLUME
57. On the collineation groups associated with twisted fields,
Calcutta Math. Soc, Golden Jubilee Commemoration
Volume (1958/59), part II, Calcutta Math. Soc, Calcutta
(1963), pp. 485 497. MR 28, 3070. 809
58. On the collineation groups of certain non Desarguesian
planes, Portugal. Math. 18 (1959), 207 224. MR 24, A473. 823
59. Generalized twisted fields, Pacific J. Math. 11 (1961),
1 8. MR 23, A182. 841
60. Isotopy for generalized twisted fields, An. Acad. Brazil.
Ci. 33 (1961), 265 275. MR 25, 3070. 849
61. On the nuclei of a simple Jordan algebra, Proc. Nat.
Acad. Sci. U.S.A. 50 (1963), 446 447. MR 27, 3679. 861
62. On exceptional Jordan division algebras, Pacific J. Math.
15 (1965), 377 404. MR 32, 130. 863
63. On some properties of biabelian fields, An. Acad. Brasil.
Ci. 38 (1966), 217 221. MR 34, 7498. 891
64. On certain polynomial systems, Scripta Math. 28 (1967)
15 19. MR 35, 2865. 897
Unpublished Articles
65. Some mathematical aspects of cryptography. 903
66. (with L. J. Paige) Malcev algebras. 921
Acknowledgments 935
xvi COLLECTED MATHEMATICAL PAPERS
|
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title | A. Adrian Albert collected mathematical papers |
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title_full | A. Adrian Albert collected mathematical papers 2 Nonassociative algebras and miscellany Richard E. Block ... ed. |
title_fullStr | A. Adrian Albert collected mathematical papers 2 Nonassociative algebras and miscellany Richard E. Block ... ed. |
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title_short | A. Adrian Albert |
title_sort | a adrian albert collected mathematical papers nonassociative algebras and miscellany |
title_sub | collected mathematical papers |
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