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Erschienen in:
01.01.2006 | Original Paper
Weak \((\mathfrak{m},\;\mathfrak{n})\)-distributivity of lattice ordered groups and of generalized MV-algebras
Erschienen in: Soft Computing | Ausgabe 2/2006
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Abstract
Let \(\mathfrak{m}\;{\text{and}}\;\mathfrak{n}\) be cardinals. The concept of weak \((\mathfrak{m},\;\mathfrak{n})\)-distributivity of Boolean algebras was intoduced by Sikorski. In the present paper we investigate this concept for lattice ordered groups and for generalized MV-algebras. We prove that the collection of all lattice ordered groups which are weakly \((\mathfrak{m},\;\mathfrak{n})\)-distributive is a radical class. An analogous result is valid for generalized MV-algebras. A Sikorski’s result concerning Boolean algebras is extended for the case of generalized MV-algebras.