Archimedean Closed Lattice-Ordered Groups

Chen, Yuanqian; Conrad, Paul; Darnel, Michael R.

doi:10.1216/rmjm/1181069894

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2008

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Cited by 2 publications

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“…Radical classes of lattice ordered groups were studied in [1], [4], [5], [9], [10], [11], [12], [13], [14], [15], [16], [18], [21] and [22]. Radical classes of M V -algebras and their relations to radical classes of lattice ordered groups were dealt with in [17] and [19].…”

Section: Introductionmentioning

confidence: 99%

K-Radical classes and product radical classes of MV-algebras

Jakubík

2008

Mathematica Slovaca

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ABSTRACT. For an MV -algebra A let J 0 (A ) be the system of all closed ideals of A ; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV -algebras will be called a K-radical class iff, whenever A ∈ X and A 1 is an MV -algebra with J 0 (A 1 ) ∼ = J 0 (A ), then A 1 ∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that there is a one-to-one correspondence between K-radical classes of MV -algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV -algebras; product radical classes of lattice ordered groups were studied by Ton.

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Section: Introductionmentioning

confidence: 99%

K-Radical classes and product radical classes of MV-algebras

Jakubík

2008

Mathematica Slovaca

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Radical classes and weak radical mappings of GMV-algebras

Jakubík

2008

Mathematica Slovaca

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ABSTRACT. We use the concept of generalized MV -algebra (GMV -algebra, in short) in the sense of Galatos and Tsinakis; the main tool in their investigation was a truncation construction. The relations between radical classes of GMV -algebras and radical classes of lattice ordered groups are investigated in the present paper. Further, we apply the truncation construction for dealing with weak retract mappings of GMV -algebras.

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Archimedean Closed Lattice-Ordered Groups

Cited by 2 publications

References 12 publications

K-Radical classes and product radical classes of MV-algebras

K-Radical classes and product radical classes of MV-algebras

Radical classes and weak radical mappings of GMV-algebras

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