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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 -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.

Hyper BCI-algebras

Xiao Long Xin (2006)

Discussiones Mathematicae - General Algebra and Applications

We introduce the concept of a hyper BCI-algebra which is a generalization of a BCI-algebra, and investigate some related properties. Moreover we introduce a hyper BCI-ideal, weak hyper BCI-ideal, strong hyper BCI-ideal and reflexive hyper BCI-ideal in hyper BCI-algebras, and give some relations among these hyper BCI-ideals. Finally we discuss the relations between hyper BCI-algebras and hyper groups, and between hyper BCI-algebras and hyper H v -groups.

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