Some properties of skew Hurwitz series

  • A. M. Hassanein
  • Mohamed A. Farahat
Keywords: Clean rings, n-clean rings, g(x)-clean rings, (n, g(x))-clean rings, Prufer domain


In this paper we show that, if R is a ring and σ an endomorphism of R, then the skew Hurwitz series ring T = (HR, σ ) is an n-clean ring if and only if R is an n-clean ring. Moreover, if R is an integral domain and a torsion-free Z-module, then T = (HR, σ ) is a Prufer domain if and only if R is a field. Also, we investigate when the ring T = (HR, σ ) is g(x)-clean, (n, g(x))-clean and a Neat ring.