Displaying similar documents to “On the distributive radical of an Archimedean lattice-ordered group”

Higher degrees of distributivity in M V -algebras

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

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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.

Annihilators in normal autometrized algebras

Ivan Chajda, Jiří Rachůnek (2001)

Czechoslovak Mathematical Journal

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The concepts of an annihilator and a relative annihilator in an autometrized l -algebra are introduced. It is shown that every relative annihilator in a normal autometrized l -algebra 𝒜 is an ideal of 𝒜 and every principal ideal of 𝒜 is an annihilator of 𝒜 . The set of all annihilators of 𝒜 forms a complete lattice. The concept of an I -polar is introduced for every ideal I of 𝒜 . The set of all I -polars is a complete lattice which becomes a two-element chain provided I is prime. The I -polars...

The H S P -Classes of Archimedean l -groups with Weak Unit

Bernhard Banaschewski, Anthony Hager (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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W denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar H , S , and P from universal algebra are here meant in W . ℤ and ℝ denote the integers and the reals, with unit 1, qua W -objects. V denotes a non-void finite set of positive integers. Let 𝒢 ⊆ W be non-void and not { { 0 } } . We show ...

Radicals and complete distributivity in relatively normal lattices

Jiří Rachůnek (2003)

Mathematica Bohemica

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Lattices in the class ℐℛ𝒩 of algebraic, distributive lattices whose compact elements form relatively normal lattices are investigated. We deal mainly with the lattices in ℐℛ𝒩 the greatest element of which is compact. The distributive radicals of algebraic lattices are introduced and for the lattices in ℐℛ𝒩 with the sublattice of compact elements satisfying the conditional join-infinite distributive law they are compared with two other kinds of radicals. Connections between complete distributivity...