arXiv subjects

Jean B. Nganou

Publications and source records attributed to Jean B. Nganou.

4 recordsLinked to original sources

arXiv2017

Compact Hausdorff MV-algebras: Structure, Duality and Projectivity

It is proved that the category $\mathbb{EM}$ of extended multisets is dually equivalent to the category $\mathbb{CHMV}$ of compact Hausdorff MV-algebras with continuous homomorphisms, which is in turn equivalent to the category of complete and completely distributive MV-algebras with homomorphisms that reflect principal maximal ideals. Urysohn-Strauss's Lemma, Gleason's Theorem, and projective objects are also investigated for topological MV-algebras.

math.LO↗

arXiv2015

Stone MV-algebras and Strongly complete MV-algebras

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 $[0,1]$ 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.

math.LO↗

arXiv2013

Profinite MV-algebras

We characterize all profinite MV-algebras, these are MV-algebras that are inverse limits of finite MV-algebras. It is shown that these are exactly direct product of finite Łukasiewicz's chains. We also prove that the category $\mathbb{M}$ of multisets is dually equivalent to the category $\mathbb{P}$ of profinite MV-algebras and homomorphisms that reflect principal maximal ideals. Thus generalizing the corresponding result for finite MV-algebras, and finite multisets.

math.LO↗

arXiv2013

On the Chang's group of BL-algebras

For an arbitrary BL-algebra L, we construct an associated lattice Abelian group that coincides with Chang's group when the BL-algebra is an MV-algebra. We prove that the Chang's group of the MV-center of any BL- algebra L is a direct summand in the above group. We also compute examples of this group.

math.LO↗