Injective Semimodules - Revisited
Abstract
Injective modules play an important role in characterizing different classes of rings (e.g. Noetherian rings, semisimple rings). Some semirings have no non-zero injective semimodules (e.g. the semiring of non-negative integers). In this paper, we study some of the basic properties of the so called e-injective semimodules introduced by the first author using a new notion of exact sequences of semimodules. We clarify the relationships between the injective semimodules, the e-injective semimodule, and the i-injective semimodules through several implications, examples and counter examples. Moreover, we provide partial results for the so called Embedding Problem (of semimodules in injective semimodules).
Cite
@article{arxiv.1904.07708,
title = {Injective Semimodules - Revisited},
author = {Jawad Abuhlail and Rangga Ganzar Noegraha},
journal= {arXiv preprint arXiv:1904.07708},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1904.01549