Generalized skew polynomial rings

Abstract

For a totally ordered cancellative semigroup Γ \Gamma , a skew field K K , let K [ Γ ; ϕ ] K[\Gamma ;\phi ] be a skew semigroup ring. If x ∈ Γ , k ∈ K x \in \Gamma ,\,k \in K , then k x = x k x kx = x{k^x} , where k → k x k \to {k^x} is an endomorphism of K K depending on x x . Ideals of K [ Γ ; ϕ ] K[\Gamma ;\phi ] are investigated for various semigroups or groups Γ \Gamma .