Nilpotents and units in skew polynomial rings over commutative rings
Maureen T. Rimmer, Ken Pearson · Journal of the Australian Mathematical Society · 1979
Abstract Let R be a commutative ring with an automorphism ∞ of finite order n. An element f of the skew polynomial ring R[x, α] is nilpotent if and only if all coefficients of fn are nilpotent. (The case n = 1 is the well-known description of the nilpotent elements of the ordinary polynomial ring R[x].) A characterization of the units in R[x, α] is also given.