Some Properties of Faithful Locally Multiplication Modules

Volume 24 , Issue 1 , June 2022 , Pages 27-37

Authors

Adil Kadir Jabbar 1 ; Payman Mahmood Hamaali 1 ; Adham Idris Abid 2

1 Department of Mathematics, College of Science, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq

2 Department of Mathematics, College of Science Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq

DOI logo 10.17656/jzs.10867

Keywords

Abstract

An 𝑅 −module 𝑀 is called a multiplication module if each submodule of 𝑀 is a product of an ideal of 𝑅 by the module and it is called a faithful module if 𝑎𝑛𝑛(𝑀) = 0. 𝑀 is called a locally multiplication module if 𝑀𝑃 is a multiplication module for each prime ideal 𝑃 of 𝑅 (due to the local ring 𝑅𝑃 on which the module 𝑀𝑃 is defined). In this paper we explore some new properties of faithful locally multiplication modules.

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  • Published at20 June 2022

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