STAR OPERATIONS ON STRONG MORI DOMAINS

Abstract

Let D be a strong Mori domain, S(D) the set of star operations on D, and S-w (D) = {* is an element of S(D) vertical bar w <= *}. We show that vertical bar S-w(D)vertical bar = Pi vertical bar S (D-p)vertical bar, where the product is taken over all maximal t-ideals P of D; we characterize when vertical bar S-w,(D)vertical bar = 2 or 3; and we investigate S-w(D[X]), proving that vertical bar S-w(D[X1)vertical bar - vertical bar S-w(D)vertical bar when S-w(D[X]) is finite.