On derivations of EQ-algebras.

The main goal of this paper is to introduce the notions of derivations on EQ-algebras and obtain several special types of them. In this paper, we discuss some properties of useful derivations and give some characterisations of them. Then, we also show that the fixed point set of useful derivations is a good EQ-algebra. Moreover, we study simple circle dot-derivations and their adjoint derivations and prove that the fixed point set of simple circle dot-derivations and that of their adjoint derivations are order isomorphism. Furthermore, the quotient algebras induced by d-filter are studied.