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An approach to the zero-divisor question for group rings

Published online by Cambridge University Press:  26 February 2010

John Clift
John Clift
Affiliation:
Queen Mary College, London E. 1.
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Extract

G. Higman [5] first considered conditions on a group G sufficient to ensure that for any ring R with no zero-divisors the group-ring RG contains no zero-divisors. It has been shown by various authors that if G belongs to one of the classes of locally indicible groups [5], right-ordered groups [6], polycyclic groups [4] or positive one-relator groups [1] then it is enough that G should be torsionfree. The proofs rely heavily on the special properties of the classes of groups involved but it may be conjectured that it is a sufficient condition in general that G should be torsionfree and no counterexamples are known.

Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979 , pp. 88 - 93
Copyright
Copyright © University College London 1979

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References

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