This article is cited in 7 papers

Research articles

On subsemimodules of semimodules

Reza Ebrahim Atani, Shahabaddin Ebrahimi Atani

University of Guilan, Rasht, Iran

Abstract: P. J. Allen [1] introduced the notion of a $Q$-ideal and a construction process was presented by which one can build the quotient structure of a semiring modulo a $Q$-ideal. Here we introduce the notion of $Q_M$-subsemimodule $N$ of a semimodule $M$ over a semiring $R$ and construct the factor semimodule $M/N$. It is shown that this notion inherits most of the essential properties of the factor modules over a ring.

Keywords and phrases: semiring, $k$-subsemimodules, $Q_M$-subsemimodules, prime subsemimodules.

MSC: 16Y60

Received: 20.10.2008

Language: English

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