On semisimple semigroup rings
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- by Mark L. Teply, E. Geis Turman and Antonio Quesada PDF
- Proc. Amer. Math. Soc. 79 (1980), 157-163 Request permission
Abstract:
Let $\pi$ be a property of rings that satisfies the conditions that (i) homomorphic images of $\pi$-rings are $\pi$-rings and (ii) ideals of $\pi$-rings are $\pi$-rings. Let S be a semilattice P of semigroups ${S_\alpha }$. If each semigroup ring $R[{S_\alpha }](\alpha \in P)$ is $\pi$-semisimple, then the semigroup ring $R[{S_\alpha }]$ is also $\pi$-semisimple. Conditions are found on P to insure that each $R[{S_\alpha }](\alpha \in P)$ is $\pi$-semisimple whenever S is a strong semilattice P of semigroups ${S_\alpha }$ and $R[S]$ is $\pi$-semisimple. Examples are given to show that the conditions on P cannot be removed. These results and examples answer several questions raised by J. Weissglass.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 157-163
- MSC: Primary 20M25; Secondary 16A12
- DOI: https://doi.org/10.1090/S0002-9939-1980-0565329-2
- MathSciNet review: 565329