A note on zero divisors in group-rings
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- by Jacques Lewin
- Proc. Amer. Math. Soc. 31 (1972), 357-359
- DOI: https://doi.org/10.1090/S0002-9939-1972-0292957-X
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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
- P. M. Cohn, On the free product of associative rings. III, J. Algebra 8 (1968), 376–383. MR 222118, DOI 10.1016/0021-8693(68)90066-5
- A. V. Jategaonkar, Left principal ideal rings, Lecture Notes in Mathematics, Vol. 123, Springer-Verlag, Berlin-New York, 1970. MR 0263850
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- 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