Idealization and theorems of D. D. Anderson

Majid M. Ali

doi:10.1080/00927870600938837

Idealization and theorems of D. D. Anderson

Majid M. Ali^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

All rings are commutative with identity and all modules are unital. Anderson proved that a submodule N of an R-module M is multiplication (resp. join principal) if and only if 0₍₊₎N is a multiplication (resp. join principal) ideal or R(M). The idealization of M. In this article we develop more fully the tool of idealization of a module, particularly in the context of multiplication modules, generalizing Anderson's theorems and discussing the behavior under idealization of some ideals and some submodules associated with a module.

Original language	English
Pages (from-to)	4479-4501
Number of pages	23
Journal	Communications in Algebra
Volume	34
Issue number	12
DOIs	https://doi.org/10.1080/00927870600938837
Publication status	Published - Dec 1 2006

Keywords

Flat module
Idealization
Join principal submodule
Multiplication module
Projective module
Pure submodule

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927870600938837

Cite this

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KW - Join principal submodule

KW - Multiplication module

KW - Projective module

KW - Pure submodule

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Idealization and theorems of D. D. Anderson

Abstract

Keywords

ASJC Scopus subject areas

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