English

Toward Homological Characterization of Semirings by e-Injective Semimodules

Rings and Algebras 2016-08-10 v1

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.

Keywords

Cite

@article{arxiv.1608.02837,
  title  = {Toward Homological Characterization of Semirings by e-Injective Semimodules},
  author = {J. Y. Abuhlail and S. N. Il'in and Y. Katsov and T. G. Nam},
  journal= {arXiv preprint arXiv:1608.02837},
  year   = {2016}
}

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27 pages