满足素Radical条件的模与II的层构造
Modules Satisfying the Prime Radical Condition and a Sheaf Construction for Modules II
摘要：
本文继续研究满足素根条件的模（$\mathbb{P}$ -根模），这在第一部分中介绍过（见\cite{BS}）。设$R$是有单位元的交换环.本文的目的是证明$\mathbb{P}$ -根$R$ -模（具有Zerkiki拓扑）的谱理论类似于环的谱理论.首先，我们研究了$\mathbb{P}$ -根模在局部化和直和下的行为。最后，我们给出了素谱Spec $(M)$上的结构层的构造，它将代数几何中环$R$的经典结构层推广到模$M$上.
英文摘要：
In this paper we continue our study of modules satisfying the prime radical condition ($\mathbb{P}$-radical modules), that was introduced in Part I (see \cite{BS}). Let $R$ be a commutative ring with identity. The purpose of this paper is to show that the theory of spectrum of $\mathbb{P}$-radical $R$-modules (with the Zariski topology) resembles to that of rings. First, we investigate the behavior of $\mathbb{P}$-radical modules under localization and direct sums. Finally, we describe the construction of a structure sheaf on the prime spectrum Spec$(M)$, which generalizes the classical structure sheaf of the ring $R$ in Algebraic Geometry to the module $M$.
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