On semirings whose simple semimodules are projective
- Authors: Il’in S.N.1
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Affiliations:
- Lobachevskiĭ Institute of Mathematics and Mechanics
- Issue: Vol 58, No 2 (2017)
- Pages: 215-226
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171055
- DOI: https://doi.org/10.1134/S0037446617020045
- ID: 171055
Cite item
Abstract
We study the semirings whose simple semimodules are all projective. In particular, we establish that for every semiring S this condition implies the injectivity of all simple S-semimodules and show that, in contrast to the case of rings, the projectivity of all simple semimodules in general is not a left-right symmetric property.
Keywords
About the authors
S. N. Il’in
Lobachevskiĭ Institute of Mathematics and Mechanics
Author for correspondence.
Email: Sergey.Ilyin@kpfu.ru
Russian Federation, Kazan