Year: 2025
Type: article
Abstract: This paper is concerned with the properties of the prime spectrum of MV-algebras, namely the space of its prime ideals with the Zariski topology which is an important topological invariant of MV-algebras. The prime spectrum is a complete invariant in Boolean algebras, but in MV-algebras this is not the case. Nevertheless knowledge of the prime spectrum gives a lot of information: There are many properties of MV-algebras which depend only on the spectrum. We call these properties “topological” and we study them. For instance, we prove that simplicity and strong simplicity are topological as well as the class of hyperarchimedean MV-algebras and the class of regular MV-algebras, while the class of perfect MV-algebras and algebraically closed are not.
Source: Studia Logica
Institution: University of Salerno
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4410729429