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 ...