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Units of the Group Ring

Published online by Cambridge University Press:  20 November 2018

N. J. Groenewald
N. J. Groenewald*
Affiliation:
Department of Mathematics, University of Port Elizabeth, P.O. Box 1600 Port Elizabeth 6000Republic of South Africa
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If R is a ring such that x, y ∈ R and xy = 0 imply yx = 0 and G≠ 1, an ordered group, then we show that ∑ αgg is a unit in RG if and only if there exists ∑ βhh in RG such that ∑ αgβg-1 = 1 and αgβh is nilpotent whenever gh≠l. We also show that if R is a ring with no nilpotent elements ≠ 0 and no idempotents ≠ 0, 1 then RG has only trivial units. Some applications are also given.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 4 , 01 December 1980 , pp. 445 - 448
Copyright
Copyright © Canadian Mathematical Society 1980

References

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