October 16, 2025Open Access

Second semimodules over commutative semirings

Key Points

Second subsemimodules exhibit unique behavior where scalar multiplications lead to specific outcomes.
For any element in a semiring, the condition aS = S or aS = 0 defines second subsemimodules.
Semimodules provide a generalized framework for structure analysis over commutative semirings.
This study emphasizes the significance of understanding second subsemimodules to advance algebraic research.

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 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.

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Cite This Study

F. Farshadifar (Thu,) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd245 https://doi.org/https://doi.org/10.48550/arxiv.2505.09966

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