ON RIGHT f-DERIVATIONS OF INCLINE ALGEBRAS

Abstract

Abstract. In this paper, we introduce the concept of a rightderivation in incline algebras and give some properties of inclinealgebras. Also, the concept of d-ideal is introduced in an inclinealgebra with respect to right derivation. 1. IntroductionZ. Q. Cao, K. H. Kim and F. W. Roush [4] introduced the notionof incline algebras in their book and later it was developed someauthors [1, 2, 3, 5]. Ahn et al [1] introduced the notion of quotientincline and obtained the structure of incline algebras. N. O. Alshehri [3]introduced the notion of derivation in incline algebra. Incline algebra is ageneralization of both Boolean and fuzzy algebra and it is a special typeof semiring. It has both a semiring structure and a poset structure. Itcan also be used to represent automata and other mathematical systems,to study inequalities for non-negative matrices of polynomials. In thispaper, we introduce the concept of a right derivation in incline algebrasand give some properties of incline algebras. Also, the concept of d-idealis introduced in an incline algebra with respect to right derivation.2. PreliminariesAn incline algebra is a set K with two binary operations denoted by + and satisfying the following axioms:(K1) x+ y = y + x;(K2) x+ (y + z) = (x+ y) + z;