On subquasivariety lattices of some varieties related with distributive p-algebras (Q1073820)

The author examines the lattices of subquasivarieties of the varieties of distributive double p-algebras and double Heyting algebras. It is shown that neither of these two lattices satisfies a non trivial lattice identity. Furthermore, the author proves that the lattice of subquasivarieties of a variety of distributive p-algebras is either distributive or does not satisfy a non trivial lattice identity; for this result, cf. also \textit{M. P. Tropin} [Algebra Logika 22, 159-167 (1983; Zbl 0541.06008)].