Coprimely Structured Modules
Zehra Bilgin, K\"ur\c{s}at Hakan Oral
TL;DR
This paper introduces and studies coprimely structured modules over commutative rings, exploring their properties and providing results for finitely generated and multiplication modules.
Contribution
It defines coprimely structured modules and investigates their properties, offering new results for finitely generated and multiplication modules.
Findings
Characterization of coprimely structured modules
Results for finitely generated coprimely structured modules
Results for coprimely structured multiplication modules
Abstract
Let R be a commutative ring with identity. A prime submodule P of an R-module M is called coprimely structured if, whenever P is coprime to each element of an arbitrary family of submodules of M, the intersection of the family is not contained in P. An R-module M is called coprimely structured provided each prime submodule of M is coprimely structured. In this paper, properties of coprimely structured modules are examined. Severals results for coprimely structured finitely generated modules and coprimely structured multiplication modules are obtained.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic structures and combinatorial models · Advanced Topics in Algebra