Multiplication Modules and Homogeneous Idealization IV - NZJM

New Zealand Journal of Mathematics

Majid M. Ali¹ 

[1] Department of Mathematics and StatisticsSultan Qaboos UniversityP.O. Box 36, PC. 123 AlkhoudMuscat,Sultanate of Oman$$

关键词: Multiplication module;    Comultiplication module;    Projective module;    Flat module;    μ-ring;    Laskerian ring.;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Auckland * Department of Mathematics

【 摘 要 】

All rings are commutative with identity and all modules are unital.Let Rbe a ring, M an R-module and R(M), the idealization of M. Homogeneuous ideals of R(M) have the form I( + )N where I is an ideal ofR, N a submodule of M such that . In particular, is a homogeneous ideal of R(M). The purpose ofthis paper is to investigate how properties of the ideal [N:M]( + )N arerelated to those of N. We determine when R(M) is a μ-ring, stronglyLaskerin ring, Hilbert ring or satisfies Property (U) or Property (FU). Itis also shown that if all homogeneous ideals of R(M) have a certainprescribed property, then all ideals of R(M) have the same property.

【 授权许可】

Unknown