Теорема Размыслова - Кемера - Брауна для афинных PI-алгебр
https://doi.org/10.22405/2226-8383-2020-21-3-89-128
Ключевые слова
Об авторах
Александр Яковлевич Канель-БеловИзраиль
доктор физико-математических наук, федеральный профессор математики MIPT, профессор
Роуэн Луис Халли
Израиль
Список литературы
1. S.A. Amitsur, A generalization of Hilbert Nullstellensatz, Proc. Amer. Math. Soc. {bf 8} (1957) 649-656.
2. S.A. Amitsur, A note on P.I. rings, Israel J. Math.{bf 10} (1971) 210--211.
3. S.A. Amitsur and C. Procesi, Jacobson rings and Hilbert algebras with polynomial identities,
4. Ann. Mat. Pura Appl. {bf 71} (1966) 67--72.
5. S.A. Amitsur and A. Regev: P.I. algebras and their co-characters, J. of Algebra {bf 78} (1982) 248--254.
6. S.A. Amitsur and L. Small, {it Affine algebras with polynomial identities,} Supplemento ai Rendiconti del Circolo Matematico di Palermo {bf 31} (1993).
7. A. Belov, L. Bokut, L.H. Rowen, and J.T. Yu,{it The Jacobian Conjecture, together with Specht and Burnside-type problems}, Proc. Groups of Automorphisms in Birational and AffineGeometry, Springer, editors M.Zaidenberg, M. Rich, and M. Reizakis,to appear.
8. A.K. Belov and L.H. Rowen, {it Computational aspects of Polynomial Identities,} A. K. Peters (2005).
9. A. Braun, The nilpotency of the radical in a finitely generated PI-ring,J. Algebra {bf 89} (1984), 375-396.
10. M. Fayers, Irreducible Specht modules for Hecke algebras of type A,Advances in Math. {bf 193} (2005), 438--452.
11. M. Fayers, S. Lyle, S. Martin, p-restriction ofpartitions and homomorphisms between Specht modules, J. Algebra 306 (2006), 175--190.
12. N. Jacobson, {it Basic Algebra II}, secondedition, Freeman and company (1989).
13. G. D. James, {it The Representation Theory of the Symmetric Groups}, Lecture Notes in Math, Vol. 682, Springer--Verlag, New York, NY, (1978).
14. G. James and A. Mathas, {it The irreducible Specht modules in characteristic $2$}, Bull. London Math. Soc. {bf 31} (1999), 457--62.
15. G. D. James and A. Kerber, {it The Representation Theory of the Symmetric group}, Encyclopedia of Mathematics and its Applications, Vol. 16, Addison--Wesley, Reading, MA, (1981).
16. A.R Kemer, Capelli identities and nilpotence of the radical of a finitely generated PI-algebra, Dokl. Akad. Nauk SSSR {bf 255} (1980), 793-797 (Russian). English translation: Soviet Math. Dokl. {bf 22} (1980), 750-753.
17. A.R. Kemer, Ideals of identities of associative algebras, Amer. Math. Soc. Translations of monographs {bf 87} (1991).
18. A.R. Kemer, Multilinear identities of the algebras over a field of characteristic $p$, Internat. J. Algebra Comput. {5} no. 2, (1995), 189--197.
19. J. Lewin, A matrix representation for associative algebras I and II, Trans. Amer. Math. Soc. textbf{188}(2), 293--317 (1974).
20. L'vov, Unpublished (Russian).
21. I.G. Macdonald, {it Symmetric Functions and Hall Polynomials}, 2nd edition, Oxford University Press, Oxford,(1995).
22. A. Mathas, {it Iwahori--Hecke algebras and Schur algebras of thesymmetric group}, University Lecture Series 15, American Mathematical Society, Providence, RI (1999).
23. Yu.P. Razmyslov, The Jacobson radical in PI-algebras (Russian),Algebra i Logika {bf 13} (1974), 337-360. English translation: Algebra and Logika{bf 13} (1974), 192-204.
24. A. Regev, Existence of identities in $Aotimes B$, IsraelJ. Math. {bf 11} (1972), 131--152.
25. A. Regev, The representations of $S_n$ and explicit identitiesfor P.I. algebras, J. Algebra {bf 51} (1978), 25--40.
26. Richard Resco, Lance W. Small and J. T. Stafford, Krull and Global Dimensions of Semiprime Noetherian $PI$-RingsTransactions of the American Mathematical Society {bf 274, No. 1} (1982), 285--295
27. L.H. Rowen, {it Polynomial Identities in Ring Theory}, Pure and AppliedMathematics, 84. Academic Press, Inc. [Harcourt Brace Jovanovich,Publishers], New York-London, (1980).
28. L.H. Rowen, {it Ring Theory}, Vol. II. Pure and Applied Mathematics, 128. Academic Press, Inc., Boston, MA, (1988).
29. L.H. Rowen, {it {Graduate algebra: Commutative View}}, AMS Graduate Studies in Mathematics {73}, 2006.
30. L.H. Rowen, {it {Graduate algebra: Noncommutative View}}, AMS Graduate Studies in Mathe-matics textbf{91}, 2008.
31. B.E. Sagan, {it The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions}, 2nd edition, Graduate Texts in Mathematics 203, Springer-Verlag (2000).
32. A.I. Shirshov, On certain non associative nil rings and algebraic algebras (Russian), Mat. Sb. {bf 41} (1957), 381-394.
33. A.I. Shirshov, On rings with identity relations (Russian), Mat. Sb. {bf 43} (1957), 277-283.
34. Small, L.W.,newblock {em An example in PI rings},newblock J. Algebra {bf 17} (1971), 434--436.
35. K.A. Zubrilin, Algebrassatisfying Capelli identities, Sbornic Math. {bf 186} no. 3 (1995) 359-370.
Рецензия
Для цитирования:
Канель-Белов А.Я., Халли Р.Л. Теорема Размыслова - Кемера - Брауна для афинных PI-алгебр. Чебышевский сборник. 2020;21(3):89-128. https://doi.org/10.22405/2226-8383-2020-21-3-89-128
For citation:
Kanel Belov A., Rowen L. The Braun–Kemer–Razmyslov Theorem for affine PI-algebras. Chebyshevskii Sbornik. 2020;21(3):89-128. (In Russ.) https://doi.org/10.22405/2226-8383-2020-21-3-89-128