On derivations of quantales

Abstract

A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.

Keywords

• quantale
• derivation
• quantic nucleus
• pre-derivation
• quantic pre-nucleus
• 06a06
• 54a10