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Given a prime ring R, a skew g-derivation for g : R → R is an additive map f : R → R such that f (xy) = f (x)g(y)+xf (y) = f (x)y +g(x)f (y) and f (g(x)) = g(f (x)) for all x, y ∈ R. We generalize some properties of prime rings with derivations to the class of prime rings with skew derivations.In this article R denotes an associative ring with center C(R), and Z denotes the ring of integers. We recall a few concepts of ring theory.A ring R is called n-torsion-free if nx = 0 for x ∈ R implies that x = 0. A ring R is called prime if for all a, b ∈ R it follows from aRb = 0 that either a = 0 or b = 0. The commutator xy − yx is denoted by [x, y]. The main commutator identities are [xy, z] = [x, z]y + x[y, z] and [x, yz] = [x, y]z + y[x, z].An additive map D from R to R is called a derivation if D(xy) = D(x)y + xD(y) for all x, y ∈ R.We introduce the concept of skew derivation (or semiderivation) that generalizes the concept of derivation which was introduced in [1].

In this study, we introduce the notion of * and +-symmetric bi-multipliers in incline algebras and research some related properties. Also, we define kernel of * and +-symmetric bi-multipliers in incline algebras. Additionally, we state some properties of these * and +-symmetric bi-multipliers in integral incline algebras.

In this paper, we introduce the notion of derivation of pseudo BCI-algebras and investigate some related properties.

We study hyper pseudo BCC-algebras which are a common generalization of hyper BCC-algebras and hyper BCK-algebras. In particular, we introduce different notion of hyper pseudo BCC-algebras and describe the relationship among them. Then, by choosing one of these definitions, we investigate for its related properties.