Toward homological structure theory of semimodules: On semirings all of whose cyclic semimodules are projective
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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.About:
This article is published in Journal of Algebra.The article was published on 2017-04-15 and is currently open access. It has received 16 citations till now. The article focuses on the topics: Endomorphism.read more
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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.
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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.
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On congruence-semisimple semirings and the K0-group characterization of ultramatricial algebras over semifields
TL;DR: In this article, the pre-ordered abelian Grothendieck groups K 0 (S ) and S K 0(S ) of the isomorphism classes of the finitely generated projective and strongly projective S-semimodules, respectively, over an arbitrary semiring S, are shown to be complete invariants of ultramatricial algebras.
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Idempotence of finitely generated commutative semifields.
Vítězslav Kala,Miroslav Korbelář +1 more
TL;DR: In this article, it was shown that a commutative parasemifield S is additively idempotent provided that it is finitely generated as a semiring.
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On injectivity of semimodules over additively idempotent division semirings and chain MV-semirings
TL;DR: In this article, the authors give a characterization of injective semimodules over additively idempotent semirings, and give an explicit construction of the injective hulls of semi-modules.
References
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Book
Semirings and their Applications
TL;DR: In this paper, the authors define Hemirings and semirings as "sets and relations with values with values in a semiring" and define a set of conditions on semimodal construction.
Book
Categories and Sheaves
正樹 柏原,Pierre Schapira +1 more
TL;DR: The Language of Categories as mentioned in this paper is a language of categories that includes the following features: limits, filters and filters, generators and representability, localization, and localisation.
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First steps in tropical geometry
TL;DR: Tropical algebraic geometry is the geometry of the tropical semiring as mentioned in this paper, where the objects are polyhedral cell complexes which behave like complex algebraic varieties and have a complete description of the families of quadrics through four points in the tropical projective plane and a counterexample to the incidence version of Pappus' Theorem.
Book
The q-theory of Finite Semigroups
John Rhodes,Benjamin Steinberg +1 more
TL;DR: The q-theory of finite semigroups as mentioned in this paper is a theory that provides a unifying approach to finite semigroup theory via quantization, and it is the only contemporary exposition of the complete theory of the complexity of finite semiigroups.