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}
}
Comments
27 pages