Spectra and reticulation of semihoops

Abstract

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 T0{T}_{0} topological space and that the maximal spectrum is a compact T2{T}_{2} 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.

Keywords

• semihoop
• prime filter
• maximal filter
• spectra
• reticulation
• bounded distributive lattice
• 06f35
• 03g25
• 08a72