Homoderivations on Lattice Structures

Abstract

Lattice theory is a central area of order theory with wide applications in algebra and computer science. In this dissertation, we study derivations on lattices and their recent generalization, called homoderivations, which combine properties of derivations and meet-homomorphisms. We investigate fundamental properties, characterizations, and special subclasses such as isotone homoderivations, and we study their relationships with classical derivations. Several examples are provided to illustrate the main results. Finally, we summarize the structure of the thesis and the main contributions.