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Some Properties of Faithful Locally Multiplication Modules
Adil Kadir Jabbar1* , Payman Mahmood Hamaali2 & Adham Idris Abid3 

1,2 Department of Mathematics, College of Science, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq 
3Department of Mathematics, College of Science Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq 

*Corresponding author Email: 

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.

Key Words: multiplication module, faithful module, locally multiplication module, prime submodule. 
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