[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c180332

ON PRIME SUBMODULES OF A FINITELY GENERATED PROJECTIVE MODULE OVER A COMMUTATIVE RING

Nekooei, Reza (Department of Pure Mathematics Faculty of Mathematics and Computer Shahid Bahonar University of Kerman)
Pourshafiey, Zahra (Faculty of Mathematics and Computer Shahid Bahonar University of Kerman)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.3, 2019 , pp. 729-741 More about this Journal

Abstract

In this paper we give a full characterization of prime submodules of a finitely generated projective module M over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of a finitely generated projective module and characterize the minimal primary decomposition of this submodule. Finally, we characterize the radical of an arbitrary submodule of a finitely generated projective module M and study submodules of M which satisfy the radical formula.

Keywords

projective module; primary decomposition; Dedekind domain; prime submodule; radical of submodule; radical formula;

Citations & Related Records

Reference

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