SEMIPRIME SUBMODULES OF GRADED MULTIPLICATION MODULES
نویسندگان
چکیده
منابع مشابه
On graded almost semiprime submodules
Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with a non-zero identity and $M$ be a graded $R$-module. In this article, we introduce the concept of graded almost semiprime submodules. Also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.
متن کاملPure Submodules of Multiplication Modules
The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...
متن کاملOn the Prime Submodules of Multiplication Modules
By considering the notion of multiplication modules over a commutative ring with identity, first we introduce the notion product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module. Finally, we state and prove a version of Nakayama lemma for multiplication modules and find some related basic results. 1. Introduction. Let R b...
متن کاملon graded almost semiprime submodules
let $g$ be a group with identity $e$. let $r$ be a $g$-graded commutative ring with a non-zero identity and $m$ be a graded $r$-module. in this article, we introduce the concept of graded almost semiprime submodules. also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.
متن کاملA note on primary-like submodules of multiplication modules
Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly. In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2012
ISSN: 0304-9914
DOI: 10.4134/jkms.2012.49.2.435