Some remarks on affine rings

Montgomery, S.; Small, L. W.

doi:10.1090/S0002-9939-1986-0861745-5

Some remarks on affine rings
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by S. Montgomery and L. W. Small PDF

Proc. Amer. Math. Soc. 98 (1986), 537-544 Request permission

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

J. Alev, Sur l’extension $R^{G}\hookrightarrow R$, Paul Dubreil and Marie-Paule Malliavin algebra seminar, 35th year (Paris, 1982) Lecture Notes in Math., vol. 1029, Springer, Berlin, 1983, pp. 267–282 (French). MR 732479, DOI 10.1007/BFb0098935
M. Cohen and S. Montgomery, Group-graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), no. 1, 237–258. MR 728711, DOI 10.1090/S0002-9947-1984-0728711-4
Martin Lorenz and D. S. Passman, Prime ideals in crossed products of finite groups, Israel J. Math. 33 (1979), no. 2, 89–132. MR 571248, DOI 10.1007/BF02760553
Marie-Paule Malliavin-Brameret, Dimension de Gelfand-Kirillov des algèbres à identités polynomiales, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 13, Ai, A679–A681. MR 401827
Susan Montgomery, Prime ideals in fixed rings, Comm. Algebra 9 (1981), no. 4, 423–449. MR 605031, DOI 10.1080/00927878108822591

Trace functions and affine fixed rings in non-commutative rings

S. Montgomery, Group actions on rings: some classical problems, Methods in ring theory (Antwerp, 1983) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 129, Reidel, Dordrecht, 1984, pp. 327–346. MR 770602, DOI 10.1016/0012-365x(83)90051-1
S. Montgomery and L. W. Small, Fixed rings of Noetherian rings, Bull. London Math. Soc. 13 (1981), no. 1, 33–38. MR 599637, DOI 10.1112/blms/13.1.33
S. Montgomery and L. W. Small, Integrality and prime ideals in fixed rings of P.I. rings, J. Pure Appl. Algebra 31 (1984), no. 1-3, 185–190. MR 738213, DOI 10.1016/0022-4049(84)90084-7
D. S. Passman, Fixed rings and integrality, J. Algebra 68 (1981), no. 2, 510–519. MR 608548, DOI 10.1016/0021-8693(81)90277-5
L. W. Small, Rings satisfying a polynomial identity, Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen [Lecture Notes in Mathematics at the University of Essen], vol. 5, Universität Essen, Fachbereich Mathematik, Essen, 1980. Written from notes taken by Christine Bessenrodt. MR 601386