نتایج جستجو برای: primary Zariski topology
تعداد نتایج: 708371 فیلتر نتایج به سال:
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...
In this paper, we introduce Inverse topology in a BL-algebra A and prove the set of all minimal prime filters of A, namely Min(A) with the Inverse topology is a compact space, Hausdorff, T0 and T1-Space. Then, we show that Zariski topology on Min(A) is finer than the Inverse topology on Min(A). Then, we investigate what conditions may result in the equivalence of these two topologies. Finally,...
Let G be a group with identity e. Let R be a G-graded commutative ring and let M be a graded R-module. The graded classical prime spectrum Cl.Specg(M) is defined to be the set of all graded classical prime submodule of M. The Zariski topology on Cl.Specg(M); denoted by ϱg. In this paper we establish necessary and sufficient conditions for Cl.Specg(M) with the Zariski topology to be a Noetherian...
In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...
$r$-module. in this paper, we explore more properties of $max$-injective modules and we study some conditions under which the maximal spectrum of $m$ is a $max$-spectral space for its zariski topology.
We de ne a Grothendieck topology on the category of schemes whose associated sheaf theory coincides in many cases with the Zariski topology. We also give some indications of possible advantages this new topology has over the Zariski topology.
1 Algebraic sets, affine varieties, and the Zariski topology 4 1.1 Algebraic sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Hilbert basis theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Zariski topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Proof that affine algebraic sets form closed sets on a t...
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