Homoderivations on a Lattice

Abstract

In this paper, the concept of homoderivation on a lattice as a combination of two concepts of meet-homomorphisms and derivations is introduced. Somecharacterizations and properties of homoderivations are provided. The relationshipbetween derivations and homoderivations on a lattice is established. Also, an interesting class of homoderivations namely isotone homoderivations is studied. A characterization of the isotone homoderivations in terms of the meet-homomorphisms is given. Furthermore, a sufficient condition for a homoderivation to become isotonic is established.

Key words and phrases. Lattice, derivation, homoderivation, isotone homoderivation.

2000 Mathematics Subject Classification. 03G10, 06B05, 06B10, 06B99