Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some remarks on affine rings

Authors: S. Montgomery and L. W. Small
Journal: Proc. Amer. Math. Soc. 98 (1986), 537-544
MSC: Primary 16A38; Secondary 16A72
MathSciNet review: 861745
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Various topics on affine rings are considered, such as the relationship between Gelfand-Kirillov dimension and Krull dimension, and when a "locally affine" algebra is affine. The dimension result is applied to study prime ideals in fixed rings of finite groups, and in identity components of group-graded rings.

References [Enhancements On Off] (What's this?)

  • [1] J. Alev, Sur l'extension $ {R^G} \hookrightarrow R$ (Séminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin, Paris, 1982), Lecture Notes in Math., vol. 1029, Springer-Verlag, New York, 1983, pp. 267-282. MR 732479 (85j:16050)
  • [2] M. Cohen and S. Montgomery, Group-graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), 237-258. MR 728711 (85i:16002)
  • [3] M. Lorenz and D. S. Passman, Prime ideals in crossed products of finite groups, Israel J. Math. 33 (1979), 89-132. MR 571248 (82k:16042a)
  • [4] M.-P. Malliavin, Dimension de Gelfand-Kirillov des algèbres a identites polynomiales, C. R. Acad. Sci. Paris Ser. A 282 (1976), 679-681. MR 0401827 (53:5654)
  • [5] S. Montgomery, Prime ideals infixed rings, Comm. Algebra 9 (1981), 423-449. MR 605031 (82c:16034)
  • [6] -, Trace functions and affine fixed rings in non-commutative rings (Séminaire d'Algèbre Paul Dubriel et Marie-Paule Malliavin, Paris, 1981), Lecture Notes in Math., vol. 924, Springer-Verlag, New York, 1982, pp. 356-374.
  • [7] -, Group actions on rings: Some classical problems, Methods in Ring Theorey (F. Van Oystaeyen, ed.), Proc. 1983 NATO A.S.I., Reidel, Dordrecht, 1984, pp. 327-346. MR 770602 (86d:16042)
  • [8] S. Montgomery and L. W. Small, Fixed rings of Noetherian rings, Bull. London Math. Soc. 13 (1981), 33-38. MR 599637 (82a:16033)
  • [9] -, Integrality and prime ideals in fixed rings of PI rings, J. Pure Appl. Algebra 31 (1984), 185-190. MR 738213 (85i:16020)
  • [10] D. S. Passman, Fixed rings and integrality, J. Algebra 68 (1981), 510-519. MR 608548 (83k:16026a)
  • [11] L. W. Small, Rings satisfying a polynomial identity, Lecture Notes, Universitat Essen, 1980. MR 601386 (82j:16028)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A38, 16A72

Retrieve articles in all journals with MSC: 16A38, 16A72

Additional Information

Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society