Subdirectly irreducible doublep-algebras of finite range

Abstract

In the last years the subdirecfly irreducible double p-algebras have been studied intensively. The first attempt to characterize them has been made by the author [8] giving a description of subdirectly irreducible double Stone algebras. Later, R. Beazer [1] characterized the distributive simple double p-algebras. Recently, B. Davey [3] has given a characterization of finite distributive subdirectly irreducible double p-algebras, and simultaneously, A. Romanowska and R. Freese [12] have characterized the modular subdirectly irreducible double p-algebras of finite length. In [9], we generalized these results to the class of double p-algebras with an Ns-frame. B. Davey [3] and P. KiShler [10] constructed interesting examples of infinite distributive subdirectly irreducible double palgebras. A. Romanowska and R. Freese [12] pointed out that the McKenzie's [11] splitting lattices provide examples of finite nonmodular subdirectly irreducible double p-algebras. They asked after their characterization. In this note we give an answer to this question presenting a characterization of (nonmodular) subdirectly irreducible double p-algebras of finite range.