Modules whose certain submodules are prime.
type: Item
instance of: scholarly article
title: Modules whose certain submodules are prime.
zbMATH Open document ID: 1081.16008
author: H. Koohy
author: M. Behboodi
author: O. A. S. Karamzadeh
published in: Vietnam Journal of Mathematics
publication date: 2005-05-06T00:00:00Z
review text: Throughout \(R\) is a commutative ring with identity and all modules are unital \(R\)-modules. A non-zero module \(M\) is called prime if its zero submodule is prime, i.e., if \(x\in M\) and \(r\in R\) with \(rx=0\), then \(x=0\) or \(rM=0\). A proper submodule \(N\) of a module \(M\) is called a prime submodule of \(M\) if \(M/N\) is a prime module. A module \(M\) is called fully prime if every proper submodule is a prime submodule. The authors show that a module \(M\) is fully prime if and only if \(M\) is homogeneous semisimple. Modules in which non-zero direct summands are prime are also characterized. For a one-dimensional Noetherian domain \(R\), the modules in which the zero submodule is the only prime submodule are determined.
reviewed by: Iuliu Crivei
Mathematics Subject Classification ID: 16D80
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 16D70
zbMATH DE Number: 2166020
zbMATH Keywords: fully prime modules
zbMATH Keywords: fully semiprime modules
zbMATH Keywords: direct summands
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2166020