Valuation ideals and primary w-ideals

摘要

Let D be an integral domain, V (D) (resp., t-V (D)) be the set of all valuation (resp., t-valuation) ideals of D, and w-P(D) be the set of primary w-ideals of D. Let D[X] be the polynomial ring over D, c(f) be the ideal of D generated by the coefficients of f is an element of D[X], and N-v = {f is an element of D[X] | c(f)(v) = D}. In this paper, we study integral domains D in which w-P(D) subset of t-V (D), t-V (D) subset of w-P(D), or t-V (D) = w-P(D). We also study the relationship between t-V (D) and V (D[X] Nv), and characterize when t-V (A + XB[X]) subset of w-P(A + XB[X]) holds for a proper extension A subset of B of integral domains.