Computing Intersections, Dual and Divisorial Closure of Ideals in A Class of Rings

Abstract

Let D be an integral domain, X an indeterminate over D and let n be a positive integer. The set {a₀ + a₁Xⁿ + a₂X³ + ... a_nXⁿ|a_i ∈ D} is a subrings of D[X] denoted by D+XⁿD[X]. This class of subrings is studied in [1] for n = 2. In this article we find explicit formulas to compute finite intersections, dual and divisorial closure of monomial ideals of D + XⁿD[X].

Key words and phrases. Dual of ideals, v-closure, GCD domains.

1991 Mathematics Subject Classification. 13A15, 13F05