Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2019; 34(3): 729-741

Online first article July 8, 2019      Printed July 31, 2019

https://doi.org/10.4134/CKMS.c180332

Copyright © The Korean Mathematical Society.

On prime submodules of a finitely generated projective module over a commutative ring

Reza Nekooei, Zahra Pourshafiey

Shahid Bahonar University of Kerman; Shahid Bahonar University of Kerman

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

MSC numbers: 13A99, 13C10, 13C99, 13F05

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