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summary:Any finitely generated regular variety $\mathbb{V}$ of distributive double $p$-algebras is finitely determined, meaning that for some finite cardinal $n(\mathbb{V})$, any subclass $S\subseteq \mathbb{V}$ of algebras with isomorphic endomorphism monoids has fewer than $n(\mathbb{V})$ pairwise non-isomorphic members. This result follows from our structural characterization of those finitely generated almost regular varieties which are finitely determined. We conjecture that any finitely generated, finitely determined variety of distributive double $p$-algebras must be almost regular

Homomorphisms and endomorphisms in varieties of pseudocomplemented distributive lattices (with applications to Heyting algebras)