Weak relatively uniform convergences on MV-algebras

Mathematica Slovaca

Ján Jakubík¹  Štefan Černák¹ 

关键词: Lattice ordered group;    relatively uniform convergence;    weak relatively uniform convergence;    regulator;    MV-algebra;    atom;    dual atom;   

DOI  :  10.2478/s12175-012-0078-x

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

Weak relatively uniform convergences (wru-convergences, for short) in lattice ordered groups have been investigated in previous authors’ papers. In the present article, the analogous notion for MV-algebras is studied. The system s(A) of all wru-convergences on an MV-algebra A is considered; this system is partially ordered in a natural way. Assuming that the MV-algebra A is divisible, we prove that s(A) is a Brouwerian lattice and that there exists an isomorphism of s(A) into the system s(G) of all wru-convergences on the lattice ordered group G corresponding to the MV-algebra A. Under the assumption that the MV-algebra A is archimedean and divisible, we investigate atoms and dual atoms in the system s(A).

【 授权许可】

Unknown