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arXiv · 1812.08897

On strongly harmonic and Gelfand modules

Mauricio Medina-Bárcenas·Lorena Morales-Callejas·Martha Lizbeth Shaid Sandoval-Miranda·Luis Ángel Zaldívar
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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 give a characterization 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 $\Psi(M)$ defined in [arXiv:1612.07407]. Finally, we mention some open questions that arose during this investigation.

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Mauricio Medina-Bárcenas, Lorena Morales-Callejas, Martha Lizbeth Shaid Sandoval-Miranda, Luis Ángel Zaldívar. 2018-12-20. On strongly harmonic and Gelfand modules. https://arxiv.org/abs/1812.08897

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