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arXiv · 1608.02837

Toward Homological Characterization of Semirings by e-Injective Semimodules

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

In this paper, we introduce and study e-injective semimodules, in particular over additively idempotent semirings. We completely characterize semirings all of whose semimodules are e-injective, describe semirings all of whose projective semimodules are e-injective, and characterize one-sided Noetherian rings in terms of direct sums of e-injective semimodules. Also, we give complete characterizations of bounded distributive lattices, subtractive semirings, and simple semirings, all of whose cyclic (finitely generated) semimodules are e-injective.

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BibTeXRIS

J. Y. Abuhlail, S. N. Il'in, Y. Katsov, T. G. Nam. 2016-08-09. Toward Homological Characterization of Semirings by e-Injective Semimodules. https://arxiv.org/abs/1608.02837

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