Spectra and reticulation of semihoops

In this article, we further study the filter theory of semihoops. Moreover, we use the prime (maximal) filters to construct the prime (maximal) spectrum on semihoops, and prove that the prime spectrum is a compact topological space and that the maximal spectrum is a compact topological space. As an...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2022-10, Vol.20 (1), p.1276-1287
Main Authors: Tang, Yu Jie, Xin, Xiao Long, Zhou, Xin
Format: Article
Language:English
Subjects:
03G25
06F35
08A72
bounded distributive lattice
Lattices
maximal filter
prime filter
reticulation
semihoop
spectra
Topology
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Summary:In this article, we further study the filter theory of semihoops. Moreover, we use the prime (maximal) filters to construct the prime (maximal) spectrum on semihoops, and prove that the prime spectrum is a compact topological space and that the maximal spectrum is a compact topological space. As an application, in order to study the relationship between the spectrum of semihoops and the spectrum of lattices, we introduce the reticulations of semihoops and obtain some related results.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2022-0486