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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on zero divisors in group-rings


Author: Jacques Lewin
Journal: Proc. Amer. Math. Soc. 31 (1972), 357-359
MSC: Primary 20C05
DOI: https://doi.org/10.1090/S0002-9939-1972-0292957-X
MathSciNet review: 0292957
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Abstract: Let $ Z{G_1}$ and $ Z{G_2}$ be the integral group rings of groups $ {G_1}$ and $ {G_2}$ with a common normal subgroup $ H$ and let $ K$ be a subgroup of $ H$. Let $ G$ be the free product of $ {G_1}$ and $ {G_2}$ amalgamating $ K$. If $ Z{G_1}$ and $ Z{G_2}$ are integral domains and if ZH has the Ore condition then ZG is again an integral domain.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0292957-X
Keywords: Group-rings, zero divisors, free products
Article copyright: © Copyright 1972 American Mathematical Society