A new derivation of UP-algebras by means of UP-endomorphisms

Abstract

The notions of left (resp. right)-f-derivations of type I and of left (resp. right)-f-derivations of type II of UP-algebras are introduced, some useful examples are discussed, and related properties are investigated. Moreover, we show that the kernel of right-f-derivations of type I and of right-f-derivations of type II of UP-algebras is a UP-subalgebra, and also give examples to show that the the kernel of left (resp. right)-f-derivations of type I and of left (resp. right)-f-derivations of type II of UP-algebras is not a UP-ideal, the fixed set of right-f-derivations of type I and of left (resp. right)-f-derivations of type II of UP-algebras is not a UP-subalgebra, and the fixed set of left-f-derivations of type I of UP-algebras is not a UP-ideal in general.