Torsion classes of generalized Boolean algebras

Year, pages: 2012, 399 - 416

Torsion classes and radical classes of lattice ordered groups have been investigated in several papers. The notions of torsion class and of radical class of generalized Boolean algebras are defined analogously. We denote by $T_g$ and $R_g$ the collections of all torsion classes or of all radical classes of generalized Boolean algebras, respectively. Both $T_g$ and $R_g$ are partially ordered by the class-theoretical inclusion. We deal with the relation between these partially ordered collection; as a consequence, we obtain that $T_g$ is a Brouwerian lattice. W. C. Holland proved that each variety of lattice ordered groups is a torsion class. We show that an analogous result is valid for generalized Boolean algebras.

Jakubík, J. 2012. Torsion classes of generalized Boolean algebras. In Mathematica Slovaca, vol. 62, no.3, pp. 399-416. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0017-x

Jakubík, J. (2012). Torsion classes of generalized Boolean algebras. Mathematica Slovaca, 62(3), 399-416. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0017-x