Representations of Sheffer stroke algebras and Visser algebras

We introduce the notion of q'-compactness for Sheffer stroke basic algebras and Visser algebras. Our goal is to determine when induced lattice of a Sheffer stroke basic algebra and a Visser algebra is a strongly algebraically closed algebra, and we find the condition that the lattices of complete congruences relations on a Sheffer stroke basic algebra are weakly relatively pseudocomplemented. In particular, an open question proposed by A. Di-Nola, G. Georgescu and A. Iorgulescu about the connections of dually Brouwerian pseudo-BL-algebras with other algebraic structures in Di Nola et al. (Mult Val Logic 8:717-750, 2002) is answered.