The spectrum problem for $\ell$-groups and for MV-algebras: a categorical approach
Rings and Algebras
2023-03-21 v1
Abstract
As a main result, we characterize prime spectra of abelian lattice ordered groups. Further we introduce some categories based on spectral spaces, lattices and Priestley spaces, and we relate these categories with each other and with the category of presented MV-algebras, by means of functors. We turn to lattices and offer a simple characterization of 1) maps whose Stone dual preserves closed sets, and 2) closed epimorphisms between distributive lattices as well as their Stone duals. We have a characterization of the variety generated by the Chang MV-algebra and we study this variety. Next we generalize the results to every variety generated by a Komori chain. Finally we discuss homogeneous polynomials in MV-algebras.
Keywords
Cite
@article{arxiv.2303.10208,
title = {The spectrum problem for $\ell$-groups and for MV-algebras: a categorical approach},
author = {Giuseppina Gerarda Barbieri and Antonio Di Nola and Giacomo Lenzi},
journal= {arXiv preprint arXiv:2303.10208},
year = {2023}
}