Weak \((\mathfrak{m},\mathfrak{n})\)-distributivity of lattice ordered groups and of generalized MV-algebras
For any cardinals \(\mu\) and \(\mu'\), Sikorski defined weak \((\mu,\mu')\)-distributivity in the framework of Boolean algebras. The author investigates this notion in the wider context of GMV-algebras (i.e., the noncommutative generalization of MV-algebras) and of lattice-ordered groups. In particular, he proves that lattice-ordered groups which are weakly \((\mu,\mu')\)-distributive form a radical class. A similar result is proved for GMV-algebras. For background on MV-algebras see the monograph by \textit{R. L. O. Cignoli}, \textit{I. M. L. D'Ottaviano} and \textit{D. Mundici} [Algebraic foundations of many-valued reasoning, Dordrecht: Kluwer Academic Publishers (2000; Zbl 0937.06009)].
scientific article; zbMATH DE number 5009507