Deductive systems of a cone algebra — II: Isomorphism theorem

Mathematica Slovaca

N. Subrahmanyam¹ 

关键词: cone algebra;    semi-â„“g-cone;    pseudo MV-algebra;    deductive system;    â„“-group;    ideal;   

DOI  :  10.2478/s12175-008-0101-4

学科分类：数学（综合）

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

【 摘 要 】

We prove that there is an isomorphism φ of the lattice of deductive systems of a cone algebra onto the lattice of convex ℓ-subgroups of a lattice ordered group (determined by the cone algebra) such that for any deductive system A of the cone algebra, A is respectively a prime, normal or polar if and only if φ(A) is a prime convex ℓ-subgroup, ℓ-ideal or polar subgroup of the ℓ-group, thus generalizing and extending the result of Rachůnek that the lattice of ideals of a pseudo MV-algebra is isomorphic to the lattice of convex ℓ-subgroups of a unital lattice ordered group.

【 授权许可】

Unknown