Radical classes of generalized Boolean algebras

Ján Jakubík

Displaying similar documents to “Radical classes of generalized Boolean algebras”

Radical classes of distributive lattices having the least element

Ján Jakubík (2002)

Mathematica Bohemica

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Let $𝒟$ be the system of all distributive lattices and let $𝒟_{0}$ be the system of all $L \in 𝒟$ such that $L$ possesses the least element. Further, let $𝒟_{1}$ be the system of all infinitely distributive lattices belonging to $𝒟_{0}$ . In the present paper we investigate the radical classes of the systems $𝒟$ , $𝒟_{0}$ and $𝒟_{1}$ .

Radical classes of complete lattice ordered groups

Ján Jakubík (1999)

Mathematica Slovaca

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On some types of radical classes

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

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Let $𝔪$ be an infinite cardinal. We denote by $C_{𝔪}$ the collection of all $𝔪$ -representable Boolean algebras. Further, let $C_{𝔪}^{0}$ be the collection of all generalized Boolean algebras $B$ such that for each $b \in B$ , the interval $[0, b]$ of $B$ belongs to $C_{𝔪}$ . In this paper we prove that $C_{𝔪}^{0}$ is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized $M V$ -algebras.