论文标题
Zariski拓扑在二次模块的频谱上
The Zariski topology on the secondary like spectrum of a module
论文作者
论文摘要
让$ r $为具有团结的换向戒指，而$ m $为左$ r $ - 模块。我们将$ m $的二级频谱定义为所有二次subsodules $ k $ $ m $的集合，以便$ ann_r（soc（k））= \ sqrt {ann_r（k）} $，我们用$ spec^l（m）$表示它。在本文中，我们在第二频谱$ spec^s（m）$上引入了$ spec^l（m）$作为子空间拓扑的拓扑，并研究了该拓扑的几个拓扑结构。
Let $R$ be a commutative ring with unity and $M$ be a left $R$-module. We define the secondary-like spectrum of $M$ to be the set of all secondary submodules $K$ of $M$ such that $Ann_R(soc(K))=\sqrt{Ann_R(K)}$, and we denote it by $Spec^L(M)$. In this paper, we introduce a topology on $Spec^L(M)$ having the Zariski topology on the second spectrum $Spec^s(M)$ as a subspace topology, and study several topological structures of this topology.
