# Multiplication modules and homogeneous idealization

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R(M), the idealization of M. Homogeneous ideals of R (M) have the form I(+N where I is an ideal of R, N a submodule of M and IM ⊆ N. The purpose of this paper is to investigate how properties of a homogeneous ideal I(+)N of R (M) are related to those of I and N. We show that if M is a multiplication R-module and I(-))N is a meet principal (join principal) homogeneous ideal of R (M) then these properties can be transferred to I and N. We give some conditions under which the converse is true. We also show that I(-)N is large (small) if and only if N is large in M (I is a small ideal of R).

Original language English 249-270 22 Beitrage zur Algebra und Geometrie 47 1 Published - 2006

### Fingerprint

Multiplication Module
Module
Ring
Unital
Converse
Join
Multiplication
If and only if

### Keywords

• Idealization
• Join principal submodule
• Large submodule
• Meet principal module
• Multiplication module
• Small submodule

### ASJC Scopus subject areas

• Algebra and Number Theory
• Geometry and Topology

### Cite this

In: Beitrage zur Algebra und Geometrie, Vol. 47, No. 1, 2006, p. 249-270.

Research output: Contribution to journalArticle

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