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On some types of radical classes

Authors:	Ján Jakubík

Institution:	(1) Matematicky ústav SAV, Grešákova 6, 040 01 Košice, Slovakia

Abstract:	Let $\mathfrak{m}$ be an infinite cardinal. We denote by $C_\mathfrak{m}$ the collection of all $\mathfrak{m}$ -representable Boolean algebras. Further, let $C_\mathfrak{m}^0$ be the collection of all generalized Boolean algebras B such that for each b ∈ B, the interval 0, b] of B belongs to $C_\mathfrak{m}$ . In this paper we prove that $C_\mathfrak{m}^0$ is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized MV-algebras. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-032002. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information.

Keywords:	Boolean algebra generalized Boolean algebra gif" alt="$$ \mathfrak{m} -representability" target="_blank">$$" align="middle" border="0">-representability lattice ordered group generalized MV-algebra radical class
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