نتایج جستجو برای: prime ring
تعداد نتایج: 163898 فیلتر نتایج به سال:
a module m is called epi-retractable if every submodule of m is a homomorphic image of m. dually, a module m is called co-epi-retractable if it contains a copy of each of its factor modules. in special case, a ring r is called co-pli (resp. co-pri) if rr (resp. rr) is co-epi-retractable. it is proved that if r is a left principal right duo ring, then every left ideal of r is an epi-retractable ...
In this paper we focus on a special class of commutative local rings called SPAP-rings and study the relationship between this class and other classes of rings. We characterize the structure of modules and especially, the prime submodules of free modules over an SPAP-ring and derive some basic properties. Then we answer the question of Lam and Reyes about strongly Oka ideals fam...
The purpose of this paper is to introduce the concept graded 2-prime ideals as a new generalization prime ideals. We show that and semi-prime are different. Furthermore, we weakly also Several properties investigated. study rings in which every ideal prime, call such ring 2-P-ring. Moreover, semi-primary ideals, different concepts. In fact, semi-primary, primary equivalent over Z-graded princip...
Let R be a commutative ring with unity of characteristic r≥0 and G be a locally finite group. For each x and y in the group ring RG define [x,y]=xy-yx and inductively via [x ,_( n+1) y]=[[x ,_( n) y] , y]. In this paper we show that necessary and sufficient conditions for RG to satisfies [x^m(x,y) ,_( n(x,y)) y]=0 is: 1) if r is a power of a prime p, then G is a locally nilpotent group an...
let $l$ be a completely regular frame and $mathcal{r}l$ be the ringof continuous real-valued functions on $l$. we study the frame$mathfrak{o}(min(mathcal{r}l))$ of minimal prime ideals of$mathcal{r}l$ in relation to $beta l$. for $iinbeta l$, denoteby $textit{textbf{o}}^i$ the ideal${alphainmathcal{r}lmidcozalphain i}$ of $mathcal{r}l$. weshow that sending $i$ to the set of minimal prime ideals...
Let R be a ring with Jacobson ideal J and center C. McCoy and Montgomery introduced the concept of a p-ring (p prime) as a ring R of characteristic p such that xp = x for all x in R. Thus, Boolean rings are simply 2-rings (p = 2). It readily follows that a p-ring (p prime) is simply a ring R of prime characteristic p such that R ⊆ N + Ep, where N = {0} and Ep = {x ∈ R : xp = x}. With this as mo...
Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $sigma(I^n)$, which denoted by $Ass(A/sigma(I^n))$, stabilize to $A_{sigma}(I)$. We give some properties of the sets $S^{sigma}_{n}(I)=Ass(A/sigma(I^n))setminus A_{sigma}(I...
It is shown that a commutative Bézout ring R with compact minimal prime spectrum is an elementary divisor ring if and only if so is R/L for each minimal prime ideal L. This result is obtained by using the quotient space pSpec R of the prime spectrum of the ring R modulo the equivalence generated by the inclusion. When every prime ideal contains only one minimal prime, for instance if R is arith...
By means of a kind of new idea, we redefine some kinds of fuzzy ideals in a ring and investigate some of their related properties. The concepts of strong prime (semiprime) generalized fuzzy (bi-, quasi-) ideals in rings are introduced. In particular, we discuss the relationships between strong prime (resp., semiprime) generalized fuzzy (bi-, quasi-) ideals and prime (resp. semiprime) generalize...
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