Monoid rings and related topics

Abstract

Let ϕ be an injective endomorphism of a ring A. We denote by Aℓ[[x, ϕ] the left skew (power) series ring consisting of formal series $\sum\nolimits_{1 = 0}^\infty {a_i x^i }$ of the variable x with canonical coefficients a_i ∈ A,where addition is defined naturally and multiplication is defined by the rule xⁱ a = ϕ ⁱ(a)xⁱ.