Georgia Institute of Technology College of Sciences

Following the Hilbert Basis theorem and its applications, there has been a vast variety of studies involving the chain conditions over the polynomial or the power series rings. One type of chain condition is the Archimedean condition, which says \cap_n Rt_n = 0for any nonunit element t in the ring R. In this talk, we start with the ascending chain condition on principal ideals (ACCP) over a larger class “skew generalized power series rings”. Then we explain the relation between ACCP rings and Archimedean rings and answer partially to the question “when these properties can be lifted from the ring R to the ring R[[x; α]]? ” In particular we show that if R is an Archimedean reduced ring and satisfy ACC on annihilators, then R[[x]] is also an Archimedean reduced ring.