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arXiv · 1406.0590

On V-Semirings and Semirings all of whose Cyclic Semimodules are Injective

J. Y. Abuhlail·S. N. Il'in·Y. Katsov·T. G. Nam
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Abstract

In this paper, we introduce and study V- and CI-semirings---semirings all of whose simple and cyclic, respectively, semimodules are injective. We describe V-semirings for some classes of semirings and establish some fundamental properties of V-semirings. We show that all Jacobson-semisimple V-semirings are V-rings. We also completely describe the bounded distributive lattices, Gelfand, subtractive, semisimple, and anti-bounded, semirings that are CI-semirings. Applying these results, we give complete characterizations of congruence-simple subtractive and congruence-simple anti-bounded CI-semirings which solve two earlier open problems for these classes of CI-semirings.

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J. Y. Abuhlail, S. N. Il'in, Y. Katsov, T. G. Nam. 2014-06-03. On V-Semirings and Semirings all of whose Cyclic Semimodules are Injective. https://arxiv.org/abs/1406.0590

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