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Currently displaying 1 – 20 of 257

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On algebraic operations of a lattice-ordered group

Ján Jakubík — 1979

Colloquium Mathematicae

Projectable kernel of a lattice ordered group

Ján Jakubik — 1982

Banach Center Publications

Convex isomorphisms of Archimedean lattice ordered groups.

Ján Jakubík — 1998

Mathware and Soft Computing

This paper contains a result of Cantor-Bernstein type concerning archimedean lattice ordered groups.

On absolute retracts and absolute convex retracts in some classes of l-groups

Ján Jakubík — 2003

Discussiones Mathematicae - General Algebra and Applications

By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.

Isomorphisms of direct products of lattice-ordered groups

Ján Jakubík — 2004

Discussiones Mathematicae - General Algebra and Applications

In this paper we investigate sufficient conditions for the validity of certain implications concerning direct products of lattice-ordered groups.

On the lattice of additive hereditary properties of finite graphs

Ján Jakubík — 2002

Discussiones Mathematicae - General Algebra and Applications

In this paper it is proved that the lattice of additive hereditary properties of finite graphs is completely distributive and that it does not satisfy the Jordan-Dedekind condition for infinite chains.

On chains in $M V$ -algebras

Ján Jakubík — 2001

Mathematica Slovaca

Radical classes of complete lattice ordered groups

Ján Jakubík — 1999

Mathematica Slovaca

On a cancellation rule for subdirect products of lattice ordered groups and of $GMV$ -algebras

Ján Jakubík — 2007

Mathematica Slovaca

Convergences on lattice ordered groups with a finite number of disjoint elements

Ján Jakubík — 2006

Mathematica Slovaca

Sequential convergences on pseudo MV-algebras

Ján Jakubík — 2006

Mathematica Slovaca

Convex mappings of archimedean MV-algebras

Ján Jakubík — 2001

Mathematica Slovaca

On the Schröder-Bernstein problem for Carathéodory vector lattices

Ján Jakubík — 2009

Czechoslovak Mathematical Journal

In this note we prove that there exists a Carathéodory vector lattice $V$ such that $V ≅ V^{3}$ and $V ≇ V^{2}$ . This yields that $V$ is a solution of the Schröder-Bernstein problem for Carathéodory vector lattices. We also show that no Carathéodory Banach lattice is a solution of the Schröder-Bernstein problem.

Projectability and weak homogeneity of pseudo effect algebras

Ján Jakubík — 2009

Czechoslovak Mathematical Journal

In this paper we deal with a pseudo effect algebra $𝒜$ possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, $𝒜$ can be represented as an interval of a unital partially ordered group $G$ . We prove that $𝒜$ is projectable (strongly projectable) if and only if $G$ is projectable (strongly projectable). An analogous result concerning weak homogeneity of $𝒜$ and of $G$ is shown to be valid.

On the distributive radical of an Archimedean lattice-ordered group

Ján Jakubík — 2009

Czechoslovak Mathematical Journal

Let $G$ be an Archimedean $ℓ$ -group. We denote by $G^{d}$ and $R_{D} (G)$ the divisible hull of $G$ and the distributive radical of $G$ , respectively. In the present note we prove the relation ${(R_{D} (G))}^{d} = R_{D} (G^{d})$ . As an application, we show that if $G$ is Archimedean, then it is completely distributive if and only if it can be regularly embedded into a completely distributive vector lattice.

Direct product decompositions of bounded commutative residuated $ℓ$ -monoids

Ján Jakubík — 2008

Czechoslovak Mathematical Journal

The notion of bounded commutative residuated $ℓ$ -monoid ( $B C R$ $ℓ$ -monoid, in short) generalizes both the notions of $M V$ -algebra and of $B L$ -algebra. Let $A ̧$ be a $B C R$ $ℓ$ -monoid; we denote by $ℓ (A ̧)$ the underlying lattice of $A ̧$ . In the present paper we show that each direct product decomposition of $ℓ (A ̧)$ determines a direct product decomposition of $A ̧$ . This yields that any two direct product decompositions of $A ̧$ have isomorphic refinements. We consider also the relations between direct product...

Affine completeness and wreath product decompositions of lattice ordered group

Ján Jakubík — 2008

Czechoslovak Mathematical Journal

Let $Δ$ and $H$ be a nonzero abelian linearly ordered group or a nonzero abelian lattice ordered group, respectively. In this paper we prove that the wreath product of $Δ$ and $H$ fails to be affine complete.

On some types of radical classes

Ján Jakubík — 2008

Czechoslovak Mathematical Journal

Let $𝔪$ be an infinite cardinal. We denote by $C_{𝔪}$ the collection of all $𝔪$ -representable Boolean algebras. Further, let $C_{𝔪}^{0}$ be the collection of all generalized Boolean algebras $B$ such that for each $b \in B$ , the interval $[0, b]$ of $B$ belongs to $C_{𝔪}$ . In this paper we prove that $C_{𝔪}^{0}$ is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized $M V$ -algebras.

Прямые разложения частично упорядоченных групп

Ján Jakubík — 1960

Czechoslovak Mathematical Journal

Distributivity in lattice ordered groups

Ján Jakubík — 1972

Czechoslovak Mathematical Journal

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