On injectives in some varieties of Ockham algebras

Abstract

The study of bounded distributive lattices endowed with an additional dual homomorphic operation began with a paper by J. Berman [3]. Subsequently these algebras were called distributive Ockham lattices and an order-topological duality theory for them was developed by A. Urquhart [12]. In [9], M. S. Goldberg extended this theory and described the injective algebras in the subvarieties of the variety O of distributive Ockham algebras which are generated by a single subdirectly irreducible algebra. The aim here is to investigate some elementary properties of injective algebras in join reducible members of the lattice of subvarieties of Kn,1 and to give a complete description of injectivealgebras in the subvarieties of the Ockham subvariety defined by the identity x Λ f2n(x) = x.