On V-semirings and Semirings All of Whose Cyclic Semimodules Are Injective

DOI10.1080/00927872.2014.930474zbMath1335.16035arXiv1406.0590OpenAlexW1792763004MaRDI QIDQ3448531

S. N. Il'in, Tran Giang Nam, Jawad Y. Abuhlail, Yefim Katsov

Publication date: 26 October 2015

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.0590

zbMATH Keywords

unitsinjective semimodulessemisimple semiringscongruence-simple semiringssimple semimodulesGelfand semiringsantibounded semiringsCI-semiringscyclic semimodulesV-semirings

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Projectives and injectives (category-theoretic aspects) (18G05) Semirings (16Y60) Semilattices (06A12) Units, groups of units (associative rings and algebras) (16U60)

Related Items (15)

Injective semimodules-revisited ⋮ On semirings whose simple semimodules are projective ⋮ Unnamed Item ⋮ On congruence-semisimple semirings and the \(K_{0}\)-group characterization of ultramatricial algebras over semifields ⋮ Some remarks on the Jacobson radical types of semirings and related problems ⋮ Which semifields are exact? ⋮ ON SMALL SUBTRACTIVE AND PROJECTIVE SEMIMODULES OVER ZERO-SUM SEMIRING ⋮ Axiomatizability of homological classes of semimodules over semirings ⋮ Pushouts and e-projective semimodules ⋮ Toward homological characterization of semirings by e-injective semimodules ⋮ Toward homological structure theory of semimodules: on semirings all of whose cyclic semimodules are projective ⋮ On the homological classification of semirings ⋮ On injective envelopes of semimodules over semirings ⋮ On injectivity of semimodules over additively idempotent division semirings and chain MV-semirings ⋮ On semisimple semirings

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