Mathematica Slovaca | |
Deductive systems of a cone algebra — II: Isomorphism theorem | |
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
【 预 览 】
Files | Size | Format | View |
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RO201912080690724ZK.pdf | 212KB | download |