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Your search keyword '"Valuative dimension"' showing total 2 results
Start Over Descriptor "Valuative dimension" Topic 13b25
2 results on '"Valuative dimension"'

1. On the Prime Ideal Structure of Bhargava Rings.

Author

Alrasasi, I. and Izelgue, L.

Subjects
*INTEGRAL domains, *RING theory, *POLYNOMIALS, *LOCALIZATION theory, *NILPOTENT groups
Abstract

Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be x(D): = {f ∈ K[X] | ∀ a ∈ D, f(xX + a) ∈ D[X]}, where x ∈ D. A Bhargava ring over D is a subring of the ring of integer-valued polynomials over D. In this article, we study the prime ideal structure and calculate the Krull and valuative dimension of Bhargava rings over a general domain D. [ABSTRACT FROM AUTHOR]

Published
2010
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2. On the prime ideal structure of symbolic Rees algebras

Author

Samir Bouchiba and Salah Kabbaj

Subjects
Krull domain, Noetherian, 13F20, Pure mathematics, 13B25, valuative dimension, Prime ideal, 13E05, factorial domain, Commutative Algebra (math.AC), Prime (order theory), Mathematics - Algebraic Geometry, FOS: Mathematics, fourteenth problem of Hilbert, Algebraic Geometry (math.AG), Krull dimension, Mathematics, Mathematics::Commutative Algebra, 13C15, 13F15, Jaffard domain, 13C15, 13F05, 13F15, 13E05, 13F20, 13G05, 13B25, 13B30, 13B30, Mathematics - Commutative Algebra, Domain (ring theory), associated graded ring, Symbolic Rees algebra, 13F05, 13G05, Maximal ideal, Rees algebra, subalgebra of an affine domain, Dimension theory (algebra)
Abstract

This paper contributes to the study of the prime spectrum and dimension theory of symbolic Rees algebra over Noetherian domains. We first establish some general results on the prime ideal structure of subalgebras of affine domains, which actually arise, in the Noetherian context, as domains between a domain $A$ and $A[a^{-1}]$. We then examine closely the special context of symbolic Rees algebras (which yielded the first counter-example to the Zariski-Hilbert problem). One of the results states that if $A$ is a Noetherian domain and $p$ a maximal ideal of $A$, then the Rees algebra of $p$ inherits the Noetherian-like behavior of being a stably strong S-domain. We also investigate graded rings associated with symbolic Rees algebras of prime ideals $p$ such that $A_{p}$ is a rank-one DVR and close with an application related to Hochster's result on the coincidence of the ordinary and symbolic powers of a prime ideal., 12 pages

Published
2012
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