On V-semirings and Semirings All of Whose Cyclic Semimodules Are Injective
TLDR
In this paper, the authors introduce and study V- and CI-semirings, which are semirings all of whose simple and cyclic semimodules are injective.Abstract:
In this article, we introduce and study V- and CI-semirings—semirings all of whose simple and cyclic, respectively, semimodules are injective. We describe V-semirings for some classes of semirings and establish some fundamental properties of V-semirings. We show that all Jacobson-semisimple V-semirings are V-rings. We also completely describe the bounded distributive lattices, Gelfand, subtractive, semisimple, and antibounded, semirings that are CI-semirings. Applying these results, we give complete characterizations of congruence-simple subtractive and congruence-simple antibounded CI-semirings which solve two earlier open problems for these classes of CI-semirings.read more
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Journal ArticleDOI
A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).
TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Journal ArticleDOI
Toward homological structure theory of semimodules: On semirings all of whose cyclic semimodules are projective
TL;DR: In this paper, the homological structure theory of semirings and CP-semirings was introduced, and the properties of semimodules over Boolean algebras whose endomorphism semimings are projective were studied.
Journal ArticleDOI
Toward homological characterization of semirings by e-injective semimodules
TL;DR: In this article, the authors introduce and study e-injective semimodules, in particular over additively idempotent semirings, and give complete characterizations of bounded distributive lattices, subtractive semidempotents, and simple semidimodels.
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Toward Homological Characterization of Semirings by e-Injective Semimodules
TL;DR: In this article, the authors introduce and study e-injective semimodules, in particular over additively idempotent semirings, and give complete characterizations of bounded distributive lattices, subtractive semidempotents, and simple semidimodels.
Journal ArticleDOI
On injective envelopes of semimodules over semirings
TL;DR: In this paper, the existence of injective envelopes for simple semimodules, modules, additively idempotent semi-modules, and additively regular semimmodules was studied.
References
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TL;DR: In this paper, the authors define two definitions of Lattices and describe how to describe them, and how to use them to describe lattice geometry, including polynomials, identities, and infinities.
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TL;DR: Inverse semigroups as discussed by the authors are a subclass of regular semigroup classes and can be seen as semigroup amalgamations of semigroup groups, which is a special case of regular semiigroups.
Journal ArticleDOI
A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).
TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.