Abstract
Characterizations of compact Hausdorff topological MV-algebras, Stone MV-algebras, and MV-algebras that are isomorphic to their profinite completions are established. It is proved that compact Hausdorff topological MV-algebras are products (both topological and algebraic) of copies [0, 1] with the interval topology and finite Łukasiewicz chains with the discrete topology. Going one step further, we also prove that Stone MV-algebras are products (both topological and algebraic) of finite Łukasiewicz chains with the discrete topology. Finally, it is proved that an MV-algebra is isomorphic to its profinite completion if and only if it is profinite and each of its maximal ideals of finite rank is principal.
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Presented by W. McGovern.
The author acknowledges the financial support of the office of VP of DEI at the University of Oregon.
To the memory of a great friend and mentor, John V. Leahy (1937–2015)
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Nganou, J.B. Stone MV-algebras and strongly complete MV-algebras. Algebra Univers. 77, 147–161 (2017). https://doi.org/10.1007/s00012-016-0421-0
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DOI: https://doi.org/10.1007/s00012-016-0421-0