EQUATIONAL CLASS-LIKE PROPERTIES OF 0-DISTRIBUTIVE LATTICES
Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India
(Received : January 20, 2022; Revised : May 09, 2022; Accepted : August 31, 2022)
In generalizing the notion of pseudo complemented lattice, Varlet  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.
2020 Mathematical Sciences Classification: 06A06, 06A07, 06B20
Keywords and Phrases: 0-distributive lattices, 0-modular, Equational classes, Sublattices, Direct Products, Homomorphic images.
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