arXiv subjects
Publications and source records attributed to Jean B Nganou.
Complete MV-algebras are naturally equipped with frame structures. We call them MV-frames and investigate some of their main the properties as frames. We completely characterized algebraic MV-frames as well as regular MV-frames. In addition, we consider nuclei on MV-frames in general and on MV-frames of ideals of Lukasiewicz rings. Finally, we used the Chang-Mundici functor to explore the frame structures of complete unital lattice-ordered groups.
We determine the profinite completions of MV-algebras, and obtain a description that generalizes the well known profinite completions of Boolean algebras as the power sets of their Stone spaces. We also use the description found to characterize profinite MV-algebras that are isomorphic to the profinite completion of an MV-algebra. Finally, MV-algebras for which the profinite Completion and MacNeille completion are isomorphic are characterized.
If K/F is a finite abelian Galois extension of global fields whose Galois group has exponent t, we prove that there exists a short exact sequence that has as a consequence that if t is square free, then Dec(K/F)=Br_{t}(K/F) which we use to show that prime exponent division algebras over Henselian valued fields with global residue fields are isomorphic to a tensor product of cyclic algebras. Finally, we construct a counterexample to the result for higher exponent division algebras.