On strongly harmonic and Gelfand modules

Authors

Mauricio Medina-Bárcenas, Northern Illinois University
Lorena Morales-Callejas, Universidad Nacional Autónoma de México
Martha Lizbeth Shaid Sandoval-Miranda, Universidad Autónoma Metropolitana -Unidad Iztapalapa
Ángel Zaldívar-Corichi, Universidad de Guadalajara

Author ORCID Identifier

Mauricio Medina-Bárcenas:https://orcid.org/0000-0002-4911-6982

Publication Title

Communications in Algebra

ISSN

00927872

E-ISSN

15324125

Document Type

Article

Abstract

We introduce the notions of strongly harmonic and Gelfand module, as a generalization of the well-known ring theoretic case. We prove some properties of these modules and we characterize them via their lattice of submodules and their space of maximal submodules. It is also observed that, under some assumptions, the space of maximal submodules of a strongly harmonic module constitutes a compact Hausdorff space whose frame of open sets is isomorphic to the frame Ψ(M) defined in a previous work by the authors. Finally, we mention some open questions that arose during this investigation.

First Page

1985

Last Page

2013

Publication Date

5-3-2020

DOI

10.1080/00927872.2019.1710167

Keywords

Gelfand modules, normal idiom, space of maximal submodules, strongly harmonic modules

Recommended Citation

Medina-Bárcenas, Mauricio; Morales-Callejas, Lorena; Sandoval-Miranda, Martha Lizbeth Shaid; and Zaldívar-Corichi, Ángel, "On strongly harmonic and Gelfand modules" (2020). NIU Bibliography. 234.
https://huskiecommons.lib.niu.edu/niubib/234

Department

Department of Mathematical Sciences