Torsion classes of generalized Boolean algebras. (Q2883982)

The notions of a torsion class and a radical class have been originally introduced for lattice ordered groups. However, they can be also applied to other types of algebras with a suitable concept of convexity. In the present paper the author studies the radical classes and the torsion classes of generalized Boolean algebras (relatively complemented distributive lattices with a least element). He proves that a nonempty class \(X\) is a radical class if and only if it is closed under convex subalgebras and weak direct products. It is a torsion class if and only if it is a radical class closed under homomorphic images. Further, the radical class generated by an arbitrary class \(X\) is described, and similarly for the torsion classes. A proper class of torsion classes of generalized Boolean algebras is exhibited.