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

Fatemeh Rashedi

doi:10.4995/agt.2021.13225

Authors

Fatemeh Rashedi â€ŽVelayat University https://orcid.org/0000-0003-2354-7132

DOI:

https://doi.org/10.4995/agt.2021.13225

Keywords:

primary-like submodule, Zariski topology, patch-like topology

Abstract

Let R be a commutative ring with identity and M a unitary R-module. The primary-like spectrum Spec_L(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 Spec_L(M) with the patch-like topology, and show that when, Spec_L(M) with the patch-like topology is a quasi-compact, Hausdorff, totally disconnected space.

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Author Biography

Fatemeh Rashedi, â€ŽVelayat University

Department ofâ€Ž â€ŽMathematicsâ€Ž

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