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Decomposition of ℓ -group-valued measures

Giuseppina Barbieri, Antonietta Valente, Hans Weber (2012)

Czechoslovak Mathematical Journal

We deal with decomposition theorems for modular measures μ : L → G defined on a D-lattice with values in a Dedekind complete ℓ -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete ℓ -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition for ℓ -group-valued...

Dimension in algebraic frames

Jorge Martinez (2006)

Czechoslovak Mathematical Journal

In an algebraic frame L the dimension, dim ( L ) , is defined, as in classical ideal theory, to be the maximum of the lengths n of chains of primes p 0 < p 1 < ⋯ < p n , if such a maximum exists, and ∞ otherwise. A notion of “dominance” is then defined among the compact elements of L , which affords one a primefree way to compute dimension. Various subordinate dimensions are considered on a number of frame quotients of L , including the frames d L and z L of d -elements and z -elements, respectively. The more concrete illustrations...

Direct factors of multilattice groups. II.

Milan Kolibiar (1992)

Archivum Mathematicum

Subgroups of a directed distributive multilattice group G are characterized which are direct factors of G . The main result is formulated in Theorem 2.

Direct summands and retract mappings of generalized M V -algebras

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

In the present paper we deal with generalized M V -algebras ( G M V -algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, G M V -algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of G M V -algebras. The relations between G M V -algebras and lattice ordered groups are essential for this investigation.

Distinguished completion of a direct product of lattice ordered groups

Ján Jakubík (2001)

Czechoslovak Mathematical Journal

The distinguished completion E ( G ) of a lattice ordered group G was investigated by Ball [1], [2], [3]. An analogous notion for M V -algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group G is a direct product of lattice ordered groups G i ( i ∈ ...

Divisibility in certain automorphism groups

Ramiro H. Lafuente-Rodríguez (2007)

Czechoslovak Mathematical Journal

We study solvability of equations of the form x n = g in the groups of order automorphisms of archimedean-complete totally ordered groups of rank 2. We determine exactly which automorphisms of the unique abelian such group have square roots, and we describe all automorphisms of the general ones.

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