This article is cited in 13 papers

On the Applicability to Semirings of Two Theorems from the Theory of Rings and Modules

S. N. Il'in

Kazan State University

Abstract: Problems concerning the extension of the Baer criterion for injectivity and the embedding theorem of an arbitrary module over a ring into an injective module to the case of semirings are treated. It is proved that a semiring $S$ satisfies the Baer criterion and every $S$-semimodule can be embedded in an injective semimodule if and only if $S$ is a ring.

Keywords: Baer criterion for injectivity, embedding of modules, semiring, semimodule, semigroup, commutative monoid.

UDC: 512.552.35

Received: 12.03.2007
Revised: 03.09.2007

DOI: 10.4213/mzm4574

 English version: Mathematical Notes, 2008, 83:4, 492–499

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