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24 papers · 1 filter
Divisors on Rational Normal Scrolls
Andrew R. Kustin, Claudia Polini, Bernd Ulrich
Let be the homogeneous coordinate ring of a rational normal scroll. The ring is equal to the quotient of a polynomial ring by the ideal generated by the two by two mino…
Compositions of consistent systems of rank one discrete valuation rings
William J. Heinzer, Louis J. Ratliff, David E. Rush
Let V be a rank one discrete valuation ring (DVR) on a field F and let L/F be a finite separable algebraic field extension with [L:F] = m. The integral closure of V in L is a Dedek…
Computing j-multiplicity
Koji Nishida, Bernd Ulrich
The j-multiplicity is an invariant that can be defined for any ideal in a Noetherian local ring . It is equal to the Hilbert-Samuel multiplicity if the ideal is -primary…
The Goto numbers of parameter ideals
William Heinzer, Irena Swanson
Let Q be a parameter ideal of a Noetherian local ring (R,m). The Goto number g(Q) of Q is the largest integer g such that Q:m^g is integral over Q. We examine the values of g(Q) as…
Projective equivalence of ideals in Noetherian integral domains
William J. Heinzer, Louis J. Ratliff, David E. Rush
Let I be a nonzero proper ideal in a Noetherian integral domain R. In this paper we establish the existence of a finite separable integral extension domain A of R and a positive in…
Conjugacy classes and invariant subrings of R-automorphisms of R[x]
Jebrel M. Habeb, Mowaffaq Hajja, William J. Heinzer
We consider the group G of R-automorphisms of the polynomial ring R[x] especially in the case where R is the ring of integers modulo n. We describe conjugacy classes in G, and in t…