Residual submodules of multiplication modules

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Let R be a commutative ring with identity and M an R-module. We introduce and give some properties and characterizations of the concepts of Mcancellation, M-weak cancellation, M-meet principal, and M-weak meet principal ideals. We prove that a submodule of a faithful multiplication module is faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) if and only if its residual by a finitely generated faithful multiplication ideal is a faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) submodule.

Original languageEnglish
Pages (from-to)405-422
Number of pages18
JournalBeitrage zur Algebra und Geometrie
Volume46
Issue number2
Publication statusPublished - 2005

Fingerprint

Multiplication Module
Faithful
Finitely Generated
Multiplication
Prime Submodule
Cancellation
Commutative Ring
If and only if
Module

Keywords

  • Cancellation ideal
  • Meet-principal ideal
  • Multiplication module
  • Residual submodule

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Residual submodules of multiplication modules. / Ali, Majid M.

In: Beitrage zur Algebra und Geometrie, Vol. 46, No. 2, 2005, p. 405-422.

Research output: Contribution to journalArticle

@article{32c63946004340389f607b85422b6d98,
title = "Residual submodules of multiplication modules",
abstract = "Let R be a commutative ring with identity and M an R-module. We introduce and give some properties and characterizations of the concepts of Mcancellation, M-weak cancellation, M-meet principal, and M-weak meet principal ideals. We prove that a submodule of a faithful multiplication module is faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) if and only if its residual by a finitely generated faithful multiplication ideal is a faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) submodule.",
keywords = "Cancellation ideal, Meet-principal ideal, Multiplication module, Residual submodule",
author = "Ali, {Majid M.}",
year = "2005",
language = "English",
volume = "46",
pages = "405--422",
journal = "Beitrage zur Algebra und Geometrie",
issn = "0138-4821",
publisher = "Springer Berlin",
number = "2",

}

TY - JOUR

T1 - Residual submodules of multiplication modules

AU - Ali, Majid M.

PY - 2005

Y1 - 2005

N2 - Let R be a commutative ring with identity and M an R-module. We introduce and give some properties and characterizations of the concepts of Mcancellation, M-weak cancellation, M-meet principal, and M-weak meet principal ideals. We prove that a submodule of a faithful multiplication module is faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) if and only if its residual by a finitely generated faithful multiplication ideal is a faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) submodule.

AB - Let R be a commutative ring with identity and M an R-module. We introduce and give some properties and characterizations of the concepts of Mcancellation, M-weak cancellation, M-meet principal, and M-weak meet principal ideals. We prove that a submodule of a faithful multiplication module is faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) if and only if its residual by a finitely generated faithful multiplication ideal is a faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) submodule.

KW - Cancellation ideal

KW - Meet-principal ideal

KW - Multiplication module

KW - Residual submodule

UR - http://www.scopus.com/inward/record.url?scp=30644467347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30644467347&partnerID=8YFLogxK

M3 - Article

VL - 46

SP - 405

EP - 422

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

SN - 0138-4821

IS - 2

ER -