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Unique factorisation in P.I. group-rings

Part of: Conditions on elements Rings with polynomial identity Rings and algebras arising under various constructions

Published online by Cambridge University Press:  09 April 2009

A. W. Chatters
A. W. Chatters
Affiliation:
School of Mathematics, University Walk, Bristol BS8 ITW, England e-mail: arthur.chatters@bristol.ac.uk
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Abstract

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We shall give necessary and sufficient conditions on the ring R and the group G for the group-ring RG to be a prime P. I. ring with the unique factorisation property as defined in [5].

Keywords

Unique factorisationgroup ringspolynomial identities.

MSC classification

Secondary: 16U30: Divisibility, noncommutative UFDs 16R20: Semiprime p.i. rings, rings embeddable in matrices over commutative rings 16S34: Group rings , Laurent polynomial rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 2 , October 1995 , pp. 232 - 243
Copyright
Copyright © Australian Mathematical Society 1995

References

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[2]Brown, K. A., ‘Height one primes of polycyclic group rings’, J. London Math. Soc. (2) 32 (1985), 426–438.CrossRefGoogle Scholar
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[4]Chatters, A. W. and Clark, J., ‘Group rings which are unique factorisation rings’, Comm. Algebra 19 (1991), 585–598.Google Scholar
[5]Chatters, A. W., Gilchrist, M. P. and Wilson, D., ‘Unique factorisation rings’, Proc. Edinburgh Math. Soc. (2) 35 (1992), 255–269.Google Scholar
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