Radical classes and weak radical mappings of GMV-algebras

ABSTRACT. For an archimedean lattice ordered group G let G d and G ∧ be the divisible hull or the Dedekind completion of G, respectively. Put G d∧ = X. Then X is a vector lattice. In the present paper we deal with the relations between the relatively uniform convergence on X and the relatively uniform convergence on G. We also consider the relations between the o-convergence and the relatively uniform convergence on G. For any nonempty class τ of lattice ordered groups we introduce the notion of τ -radical class; we apply this notion by investigating relative uniform convergences.

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“…The notion of radical class of lattice ordered groups has been introduced in [11] and it was investigated in several papers.…”

Section: The C-radical Class Kmentioning

confidence: 99%

Relatively uniform convergences in archimedean lattice ordered groups

Jakubík

Černák

2010

Mathematica Slovaca

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“…The system of all congruence relations of A is usually written as Con(A); in view of the notation used in the relevant papers [11] and [12], we will write C(A) rather than Con(A). The system C(A) is partially ordered by set inclusion.…”

Section: Introductionmentioning

confidence: 99%

Banaschewski’s theorem for GMV-algebras

Jakubík

2012

Mathematica Slovaca

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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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Radical classes and weak radical mappings of GMV-algebras

Cited by 5 publications

References 20 publications

Relatively uniform convergences in archimedean lattice ordered groups

Relatively uniform convergences in archimedean lattice ordered groups

Banaschewski’s theorem for GMV-algebras

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

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