Stone MV-algebras and strongly complete MV-algebras
Stone MV-algebras and strongly complete MV-algebras
复制标题
DOI：
10.1007/s00012-016-0421-0
复制
发表时间：
2015-02
影响因子：
0.6
通讯作者：
J. B. Nganou
中科院分区：
文献类型：
--
作者：
J. B. Nganou
建立了紧Hausdorff拓扑mv -代数、Stone mv -代数和与它们的无限补全同构的mv -代数的性质。证明紧致Hausdorff拓扑v -代数是具有区间拓扑的拷贝[0,1]和具有离散拓扑的有限Łukasiewicz链的积（拓扑积和代数积）。更进一步，我们还证明了Stone mv -代数是具有离散拓扑结构的有限Łukasiewicz链的乘积（拓扑和代数）。最后，证明了一个mv -代数与它的无限补全是同构的，当且仅当它是无限的并且它的有限秩的最大理想都是主的。
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.