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Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 3, Pages 33–39 (Mi ivm8780)  

Semirings satisfying the Baer criterion

S. N. Il'in

Chair of Algebra and Mathematical Logics, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: It is well-known that for modules over rings the Baer injectivity criterion takes place. In this paper we prove that under one additional condition this criterion is also valid for modules over semirings. We prove that a semiring $S$ satisfies the Baer criterion if and only if all injective (with respect to one-sided ideals of $S$) semimodules satisfy the above condition. We propose a new method for constructing semirings satisfying the Baer criterion.

Keywords: semiring, injective semimodule, Baer criterion.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:3, 26–31

UDC: 512.558
Received: 30.01.2012

Citation: S. N. Il'in, “Semirings satisfying the Baer criterion”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 3, 33–39; Russian Math. (Iz. VUZ), 57:3 (2013), 26–31

Citation in format AMSBIB
\Bibitem{Ili13}
\by S.~N.~Il'in
\paper Semirings satisfying the Baer criterion
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 3
\pages 33--39
\mathnet{http://mi.mathnet.ru/ivm8780}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 3
\pages 26--31
\crossref{https://doi.org/10.3103/S1066369X13030031}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84876221872}


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