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Proceedings of the American Mathematical Society

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A note on zero divisors in group-rings

Author: Jacques Lewin
Journal: Proc. Amer. Math. Soc. 31 (1972), 357-359
MSC: Primary 20C05
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.

References [Enhancements On Off] (What's this?)

  • [1] P. M. Cohn, On the free product of associative rings. III, J. Algebra 8 (1968), 376-383. MR 36 #5170. MR 0222118 (36:5170)
  • [2] A. V. Jategaonkar, Left principal ideal rings, Lecture Notes in Math., no. 123, Springer-Verlag, Berlin and New York, 1970. MR 0263850 (41:8449)

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Keywords: Group-rings, zero divisors, free products
Article copyright: © Copyright 1972 American Mathematical Society

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