Stone MV-algebras and Strongly complete MV-algebras
Jean B. Nganou

TL;DR
This paper characterizes compact Hausdorff and Stone MV-algebras, showing they are products of specific chains, and establishes conditions under which MV-algebras are strongly complete, linking algebraic and topological properties.
Contribution
It provides a complete characterization of compact Hausdorff and Stone MV-algebras as products of chains and identifies criteria for strong completeness in MV-algebras.
Findings
Compact Hausdorff MV-algebras are products of [0,1] and finite chains.
Stone MV-algebras are products of finite chains.
An MV-algebra is strongly complete iff it is profinite with principal finite-rank maximal ideals.
Abstract
Compact Hausdorff topological MV-algebras and Stone MV-algebras are completely characterized. We obtain that compact Hausdorff topological MV-algebras are product (both topological and algebraic) of copies with standard topology and finite Lukasiewicz chains with discrete topology. Going one step further we also prove that Stone MV-algebras are product (both topological and algebraic) of finite Lukasiewicz chains with discrete topology. We also prove that an MV-algebra is strongly complete (isomorphic to its profinite completion) if and only if it is profinite and its maximal ideals of finite ranks are principal.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Fuzzy and Soft Set Theory
