Open Accesschains and unions of prime submodules
Author(s) -
Yasoub Shahvalizadeh
Publication year - 2019
Publication title -
journal of research in science, engineering and technology
Language(s) - English
Resource type - Journals
ISSN - 2693-8464
DOI - 10.24200/jrset.vol5iss03pp9-16
Subject(s) - prime (order theory) , mathematics , commutative ring , associated prime , ring (chemistry) , noetherian ring , prime ring , identity (music) , noetherian , pure mathematics , set (abstract data type) , commutative property , discrete mathematics , algebra over a field , combinatorics , computer science , physics , programming language , chemistry , organic chemistry , acoustics
. Let R be a commutative ring with identity and let M be a unital R-module. In this paper we study the various properties of prime submodules. Also we give a new equivalent conditions for a minimal prime submodules of an R-module to be a finite set, whenever R is a Noetherian ring. Finally we prove the Prime avoidance Theorem for modules in different states.