نتایج جستجو برای: primary ideal
تعداد نتایج: 723425 فیلتر نتایج به سال:
the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...
the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$, we mean an ideal $i$ of $r$ such that $ineq r$. we say that a proper ideal $i$ of a ring $r$ is a maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...
let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...
اساس نظریه مجموعه های ناهموار، بدین صورت است که برای هر زیرمجموعه از یک مجموعه کلی، با استفاده از یک رابه هم ارزی، یک زوج مرتب از مجموعه ها را معرفی می کند. هر موفه را به ترتیب، تقریب پایینی و بالایی می نامند. تقریب پایین از یک زیرمجموعه،اجتماع تمام عناصری از مجموعه ی کلی است که کلاس هم ارزی مربوط به آن عنصر، در زیرمجموعه ی مورد نظر قرار گیرد و همچنین، تقریب بالا از آن زیرمجموعه، اجتماع تمام عن...
The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$, we mean an ideal $I$ of $R$ such that $Ineq R$. We say that a proper ideal $I$ of a ring $R$ is a maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ Isubseteq A$ and $Ineq A$ is a prime ideal. That is, among all the proper ideals of $R$,...
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. We define the primary spectrum of $M$, denoted by $mathcal{PS}(M)$, to be the set of all primary submodules $Q$ of $M$ such that $(operatorname{rad}Q:M)=sqrt{(Q:M)}$. In this paper, we topologize $mathcal{PS}(M)$ with a topology having the Zariski topology on the prime spectrum $operatorname{Spec}(M)$ as a sub...
The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...
In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate and $ (tau,sigma)$-Boolean in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...
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