A new topology over the primary-like spectrum of a module

Abstract

Let R be a commutative ring with identity and M a unitary R-module. The primary-like spectrum SpecL(M) is the collection of all primary-like submodules Q of M, the recent generalization of primary ideals, such that M/Q is a primeful R-module. In this article, we topologies SpecL(M) with the patch-like topology, and show that when, SpecL(M) with the patch-like topology is a quasi-compact, Hausdorff, totally disconnected space.

Keywords

• primary-like submodule
• zariski topology
• patch-like topology