Here, we continue to characterize a recently introduced notion, le-modules RM over a commutative ring R with unity [A. K. Bhuniya and M. Kumbhakar, Uniqueness of primary decompositions in Laskerian le-modules, Acta Math. Hunga. 158(1) (2019) 202–215]. This paper introduces and characterizes Zariski topology on the set Spec(M) of all prime submodule elements of M. Thus, we extend many results on Zariski topology for modules over a ring to le-modules. The topological space Spec(M) is connected if and only if R/Ann(M) contains no idempotents other than 0¯ and 1¯. Open sets in the Zariski topology for the quotient ring R/Ann(M) induces a base of quasi-compact open sets for the Zariski topology on Spec(M). Every irreducible closed subset of Spec(M) has a generic point. Besides, we prove a number of different equivalent characterizations for Spec(M) to be spectral.

中文翻译：

---

在 le 模块的主要频谱上

在这里，我们继续描述一个最近引入的概念，le-modulesR米在交换环上R具有统一性 [AK Bhuniya 和 M. Kumbhakar，Laskerian le 模块中初级分解的唯一性，数学学报。洪加。 158(1) (2019) 202-215]。本文介绍并刻画了集合 Spec 上的 Zariski 拓扑(米)的所有主要子模块元素米. 因此，我们将许多关于环上模块的 Zariski 拓扑结果扩展到 le 模块。拓扑空间规范(米)当且仅当R/安（米) 不包含除0¯和1¯. Zariski 拓扑中商环的开集R/安（米) 在 Spec 上为 Zariski 拓扑引入准紧开集的基础(米). Spec的每个不可约闭子集(米)有一个通用的观点。此外，我们证明了 Spec 的许多不同的等效表征(米)成为光谱。