Twisted group rings and quasi-frobenius quotient rings

In this paper we examine when a twisted group ring,Rγ(G), has a semi-simple, artinian quotient ring. In §1 we assemble results and definitions concerning quotient rings, Ore sets and Goldie rings and then, in §2, we defineRγ(G). We prove a useful theorem for constructing a twisted group ring of a factor group and establish an analogue of a theorem of Passman. Twisted polynomial rings are discussed in §3 and I am indebted to the referee for informing me of the existence of [4]. These are used as a tool in proving results in §4.

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Semi-Prime Twisted Group Rings

Journal of the London Mathematical Society ◽

10.1112/jlms/s2-12.4.413 ◽

1976 ◽

Vol s2-12 (4) ◽

pp. 413-418 ◽

Cited By ~ 7

Author(s):

A. Reid

Keyword(s):

Group Rings ◽

Twisted Group

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CLASSICAL QUOTIENT RINGS OF GROUP RINGS

Quaestiones Mathematicae ◽

10.1080/16073606.1976.9632525 ◽

1976 ◽

Vol 1 (2) ◽

pp. 219-224

Author(s):

R. W. WILKERSON

Keyword(s):

Group Rings ◽

Quotient Rings

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A class of finite commutative rings constructed from Witt rings

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700038612 ◽

2006 ◽

Vol 73 (1) ◽

pp. 47-64 ◽

Cited By ~ 1

Author(s):

Thomas Craven ◽

Monika Vo

Keyword(s):

Quadratic Forms ◽

Special Class ◽

Algebraic Theory ◽

Commutative Rings ◽

Group Rings ◽

Integral Group ◽

Witt Rings ◽

Integral Group Rings ◽

Quotient Rings ◽

Finite Commutative Rings

Motivated by constructions of Witt rings in the algebraic theory of quadratic forms, the authors construct new classes of finite commutative rings and explore some of their properties. These rings are constructed as quotient rings of a special class of integral group rings for which the group is an elementary 2-group. The new constructions are compared to other rings in the literature.

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