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Higher degrees of distributivity in $M V$ -algebras

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

In this paper we deal with the of an $M V$ -algebra $𝒜$ , where $α$ and $β$ are nonzero cardinals. It is proved that if $𝒜$ is singular and $(α, 2)$ -distributive, then it is . We show that if $𝒜$ is complete then it can be represented as a direct product of $M V$ -algebras which are homogeneous with respect to higher degrees of distributivity.

Holland’s theorem for pseudo-effect algebras

Anatolij Dvurečenskij (2006)

Czechoslovak Mathematical Journal

We give two variations of the Holland representation theorem for $ℓ$ -groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo $M V$ -algebra can be represented as a pseudo-effect algebra or as a pseudo $M V$ -algebra of automorphisms of some antilattice or of some linearly ordered set.

Horizontal sums of basic algebras

Ivan Chajda (2009)

Discussiones Mathematicae - General Algebra and Applications

The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.

Displaying 1 – 3 of 3

Higher degrees of distributivity in M V -algebras

Holland’s theorem for pseudo-effect algebras

Horizontal sums of basic algebras

Currently displaying 1 – 3 of 3

Higher degrees of distributivity in $M V$ -algebras