This article is cited in 11 papers

$V$-semirings

S. N. Il'in

Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kazan

Abstract: We investigate the semirings over which all simple semimodules are injective. In ring and module theory, the rings with an analogous condition are called $V$-rings. Therefore it is natural to call the semirings under consideration $V$-semirings. We obtain the semiring analogs of some well-known results on $V$-rings, including an analog of Kaplansky's theorem on commutative $V$-rings.

Keywords: simple semimodule, injective semimodule, essential extension, $V$-ring.

UDC: 512.558

Received: 15.03.2011

 English version: Siberian Mathematical Journal, 2012, 53:2, 222–231

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