On the distributive radical of an Archimedean lattice-ordered group

Ján Jakubík

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

Similarity:

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

Similarity:

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

Similarity:

$W$ 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 $𝒢 \subseteq W$ be non-void and not ${{0}}$ . We show ...

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

Higher degrees of distributivity in M V -algebras

Annihilators in normal autometrized algebras

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

Higher degrees of distributivity in $M V$ -algebras

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