Chain rings of skew Laurent series (Q5950859)

Denote by \(A( (t,\varphi))\) the ring of the skew Laurent series over the coefficient ring \(A\) formed by the series \(f=\sum_{i=m}^\infty f_it^i\), \(t\) is an independent variable, \(m\) is an integer. The main result of the paper is as follows. Let \(\varphi\) be an automorphism of the ring \(A\). Then the following conditions are equivalent: (1)~\(A( (t,\varphi))\) is a right chain ring; (2)~\(A( (t,\varphi))\) is a right chain right Artinian ring; (3)~\(A\) is a right chain right Artinian ring.