Second semimodules over commutative semirings

TL;DR

This paper introduces and studies the concept of second subsemimodules in semimodules over commutative semirings, expanding the algebraic theory of semimodules with a focus on their substructure properties.

Contribution

It defines second subsemimodules in the context of semimodules over commutative semirings and explores their properties and significance.

Findings

Characterization of second subsemimodules

Conditions under which subsemimodules are second

Structural properties of second subsemimodules

Abstract

Let R be a semiring. We say that a non-zero subsemimodule S of an R-semimodule M is second if for each a \in R, we have aS = S or aS = 0. The aim of this paper is to study the notion of second subsemimodules of semimodules over commutative semirings.