ON DERIVATIONS OF LATTICES
Luca Ferrari · Pure mathematics and applications · 2001
This de nition clearly coincides with the usual (algebraic) notion of derivation when [A; +, ·] is a ring. However, it can be formally stated for every algebraic structure endowed with two binary operations. In this paper, we will consider the special case in which [A; +, ·] is a lattice, so that + and · are, respectively, the join and the meet operations. These ideas have been introduced and developed by Szasz in a series of papers (here we recall [S1, S2]), in which he established the main properties of derivations of lattices. Also Kolibiar [K] gave his contribution, for example in the study of the case of the chain of natural numbers. However, it seems that these investigations only scratched the surface of the subject.