Semigroup rings and semilattice sums of rings

Weissglass, Julian

doi:10.1090/S0002-9939-1973-0322092-4

Semigroup rings and semilattice sums of rings
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Proc. Amer. Math. Soc. 39 (1973), 471-478 Request permission

Abstract:

A generalization of the concept of a decomposition of a ring into a direct sum of ideals is introduced. The question of semisimplicity of the ring in terms of the semisimplicity of its summands is investigated. The results are applied to semigroup rings.

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Quasi-orders, generalized archimedeanness and semilattice decompositions

Julian Weissglass, Radicals of semigroup rings, Glasgow Math. J. 10 (1969), 85–93. MR 265485, DOI 10.1017/S0017089500000616