On Semi n-Absorbing Subsemimodules
Year: 2026
Type: article
Abstract: : Let be a commutative semiring with identity and an -semimodule. In this paper, we introduce and study the notion of semi- -absorbing subsemimodules, which extends the concept of semi- -absorbing submodules from module theory to the broader setting of semimodules over semirings. We obtain several fundamental characterizations of semi- -absorbingsubsemimodules in terms of annihilators, cyclic subsemimodules, and colon constructions. Their behavior is investigated under homomorphisms, intersections, and quotient semimodules, along with their stability under direct sums. A complete classification of semi- -absorbing ideals of the semiring is also provided. These results generalize and unify earlier works on -absorbing and semi- -absorbing submodules, contributing to the structural theory of semimodules over commutative semirings.
Author: Bonde, Dipak R.
Institution: Arts, Commerce and Science College, Dharangaon
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214941981