Some Properties of Faithful Locally Multiplication Modules - Jabbar, Adil Kadir; Hamaali, Payman Mahmood; Abid, Adham Idris (Sulaimani Journal for Pure and Applied Sciences, 2022)
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.
Keywords: multiplication module; Faithful module; locally multiplication module; prime submodule