منابع مشابه
Linear Groups and Group Rings
This paper consists of two parts. The first is concerned with free products in linear groups and uses the usual “ping pong” lemma and attractors to prove the results. What is new here is that we allow certain subspaces of V associated with the semisimple and generalized transvection operators to have dimensions larger than 1. The second part is concerned with applications of this machinery to i...
متن کاملA Generalization of Gröbner Basis Algorithms to Polycyclic Group Rings
It is well-known that for the integral group ring of a polycyclic group several decision problems are decidable, in particular the ideal membership problem. In this paper we define an effective reduction relation for group rings over polycyclic groups. This reduction is based on left multiplication and hence corresponds to left ideals. Using this reduction we present a generalization of Buchber...
متن کاملIntroducing Reduction to Polycyclic Group Rings - A Comparison of Methods
It is well-known that for the integral group ring of a polycyclic group several decision problems are decidable. In this paper a technique to solve the membership problem for right ideals originating from Baumslag, Cannonito and Miller and studied by Sims is outlined. We want to analyze, how these decision methods are related to Grr obner bases. Therefore, we deene eeective reduction for group ...
متن کاملGrothendieck Groups of Abelian Group Rings
Let R be a noetherian ring, and G(R) the Grothendieck group of finitely generated modules over R. For a finite abelian group n, we describe G(Rn) as the direct sum of groups G(R’). Each R’ is the form RI<,,, I/n], where n is a positive integer and Cn a primitive nth root of unity. As an application, we describe the structure of the Grothendieck group of pairs (H. u), where His an abelian group ...
متن کاملTwisted Group Rings of Metacyclic Groups
Given a finite metacyclic group G, a central extension F having the projective lifting property over all fields is constructed. This extension and its group rings are used to investigate the faithful irreducible projective representations of G and the fields over which they can be realized. A full description of the finite metacyclic groups having central simple twisted group rings over fields ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1973
ISSN: 0022-4049
DOI: 10.1016/0022-4049(73)90034-0