A new notion of semiprime submodules
Masood Aryapoor
TL;DR
This paper introduces a novel concept of semiprime submodules, establishing their equivalence to radical submodules in finitely generated modules over commutative rings, and offers new characterizations.
Contribution
It defines a new notion of semiprime submodules and links it to radical submodules, providing a fresh perspective and characterization in module theory.
Findings
Semiprime submodules are equivalent to radical submodules in finitely generated modules.
A new characterization of radical submodules is provided.
The notion enhances understanding of submodule structures in commutative algebra.
Abstract
We introduce a new concept of a semiprime submodule. We show that a submodule of a finitely generated module over a commutative ring is semiprime if and only if it is radical, that is, an intersection of prime submodules. Using our notion, we also provide a new characterization of radical submodules of finitely generated modules over commutative rings.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Control Systems Optimization · Fuzzy and Soft Set Theory