A note on twisted group rings and semilinearization

AbstractLet U(KλG) be the group of units of the infinite twisted group algebra KλG over a field K. We describe the FC-centre ΔU of U(KλG) and give a characterization of the groups G and fields K for which U(KλG) = ΔU. In the case of group algebras we obtain the Cliff-Sehgal-Zassenhaus theorem.

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Multivariate Puiseux Rings Induced by a Weierstrass System and Twisted Group Rings

Communications in Algebra ◽

10.1080/00927872.2013.816314 ◽

2014 ◽

Vol 42 (11) ◽

pp. 4619-4634 ◽

Cited By ~ 1

Author(s):

Tobias Kaiser

Keyword(s):

Group Rings ◽

Twisted Group

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Twisted group rings and quasi-frobenius quotient rings

Archiv der Mathematik ◽

10.1007/bf01229784 ◽

1975 ◽

Vol 26 (1) ◽

pp. 581-587 ◽

Cited By ~ 2

Author(s):

Andreas Horn

Keyword(s):

Group Rings ◽

Twisted Group ◽

Quotient Rings

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Twisted group rings

Communications in Algebra ◽

10.1080/00927878908823886 ◽

1989 ◽

Vol 17 (12) ◽

pp. 2923-2939 ◽

Cited By ~ 1

Author(s):

Bodo Pareigis

Keyword(s):

Group Rings ◽

Twisted Group

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Twisted group rings which are semi-prime Goldie rings

Glasgow Mathematical Journal ◽

10.1017/s0017089500002433 ◽

1975 ◽

Vol 16 (1) ◽

pp. 1-11 ◽

Cited By ~ 6

Author(s):

A. Reid

Keyword(s):

Group Ring ◽

Quotient Ring ◽

Factor Group ◽

Polynomial Rings ◽

Group Rings ◽

Twisted Group ◽

Twisted Group Ring ◽

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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