REGULAR SKEW GROUP-RINGS

被引：4

作者：

ALFARO, R

ARA, P

DELRIO, A

机构：

[1] UNIV AUTONOMA BARCELONA,DEPT MATEMAT,E-08193 BARCELONA,SPAIN

[2] UNIV MURCIA,DEPT MATEMAT,E-30001 MURCIA,SPAIN

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS | 1995年 / 58卷

关键词：

D O I：

10.1017/S1446788700038210

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a group acting on a ring R. We study the problem of determining necessary and sufficient conditions in order that the skew group ring RG be von Neumann regular. Complete characterizations are given in some particular situations, including the case where all idempotents of R are central. For a regular ring R admitting a G-invariant pseudo-rank function N, with G finite, we obtain a necessary condition for RG being regular in terms of the induced action of G on the N-completion of R.

引用

页码：167 / 182

页数：16

共 21 条

[1]

Alfaro R., States on skew group rings and fixed rings, Comm. Algebra, 18, pp. 3381-3394, (1990)

[2]

Auslander M., On regular group rings, Proc. Amer. Math. Soc., 8, pp. 658-664, (1957)

[3]

Beattie M., A generalization of the smash product of a graded ring, J. Pure Appl. Algebra, 52, pp. 219-226, (1988)

[4]

Cohen M., Montgomery S., Group-graded rings, smash products and group actions, Trans. Amer. Math. Soc., 282, pp. 237-258, (1984)

[5]

Connell I.G., On the group ring, Canad. J. Math., 15, pp. 650-685, (1963)

[6]

DeMeyer F., Some notes on the general Galois theory of rings, Osaka J. Math., 2, pp. 117-127, (1965)

[7]

Goodearl K.R., Centers of regular self-injective rings, Pacific J. Math., 76, pp. 381-395, (1978)

[8]

Von Neumann regular rings, (1979)

[9]

Goursaud J.M., Osterburg J., Pascaud J.L., Valette J., Points fixes des anneaux reguliers auto-injectifs à gauche, Comm. Algebra 9, pp. 1343-1394, (1981)

[10]

Kado J., Pseudo-rank functions on crossed products of finite groups over regular rings, Osaka J. Math., 22, 1985, pp. 821-833

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