sentences:  Choose a field "k" and a formal power series "z"=Σ"i">0"a""i""x""i" in the ring "S" of formal power series in "x" over "k" such that "z" and "x" are algebraically independent.Define "z"1 = "z" and "z""i"+1="z""i"/x–"a""i".Let "R" be the (non-Noetherian) ring generated by "x" and all the elements "z""i".