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Duo group rings. (English) Zbl 1124.16020

A ring \(R\) is said to be (i) ‘duo’ if every one-sided ideal is two-sided, and (ii) ‘reversible’ if whenever \(\alpha\beta=0\) for \(\alpha,\beta\in R\), then \(\beta\alpha=0\).
The main result of this paper states that, for the group algebra \(KG\) of a torsion group \(G\) over a field \(K\), these two properties are equivalent.

MSC:

16S34 Group rings
16U80 Generalizations of commutativity (associative rings and algebras)
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
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References:

[1] Gutan, M.; Kisielewicz, A., Reversible group rings, J. Algebra, 279, 280-291 (2004) · Zbl 1068.16033
[2] Y. Li, M.M. Parmenter, Reversible group rings over commutative rings (submitted for publication); Y. Li, M.M. Parmenter, Reversible group rings over commutative rings (submitted for publication) · Zbl 1134.16009
[3] Marks, G., Reversible and symmetric rings, J. Pure Appl. Algebra, 174, 311-318 (2002) · Zbl 1046.16015
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