EQUATIONAL CLASS-LIKE PROPERTIES OF 0-DISTRIBUTIVE LATTICES
R. Subbarayan · jnanabha · 2022
Abstract In generalizing the notion of pseudo complemented lattice, Varlet [8] introduced the notion of 0-distributive lattices. In this paper, we prove that the class of 0-distributive lattices is not an equational class, but it is an equational class-like in the sense that while an equational class is closed under the operations of subalgebras, direct products and homomorphic images, the class of 0-distributive lattices is closed under the first two operations and as far as the third one is concerned, the homomorphism should be a monomorphism. We also prove that if CS (L) is 0-semimodular then so is L.