On the prime ideal structure of Bhargava rings

I. Alrasasi; L. Izelgue

doi:10.1080/00927870902922968

On the prime ideal structure of Bhargava rings

I. Alrasasi
, L. Izelgue^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be B_x(D):= {f ∈ K[X]{pipe}∀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.

Original language	English
Pages (from-to)	1385-1400
Number of pages	16
Journal	Communications in Algebra
Volume	38
Issue number	4
DOIs	https://doi.org/10.1080/00927870902922968
State	Published - Apr 2010

Keywords

Bhargava ring
Integer-valued polynomials
Krull dimension
Localization
Prime ideal
Residue field
Valuative dimension

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927870902922968

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title = "On the prime ideal structure of Bhargava rings",

abstract = "Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be Bx(D):= \{f ∈ K[X]\{pipe\}∀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.",

keywords = "Bhargava ring, Integer-valued polynomials, Krull dimension, Localization, Prime ideal, Residue field, Valuative dimension",

author = "I. Alrasasi and L. Izelgue",

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AU - Alrasasi, I.

AU - Izelgue, L.

PY - 2010/4

Y1 - 2010/4

N2 - Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be Bx(D):= {f ∈ K[X]{pipe}∀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.

AB - Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be Bx(D):= {f ∈ K[X]{pipe}∀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.

KW - Bhargava ring

KW - Integer-valued polynomials

KW - Krull dimension

KW - Localization

KW - Prime ideal

KW - Residue field

KW - Valuative dimension

UR - https://www.scopus.com/pages/publications/77950957807

U2 - 10.1080/00927870902922968

DO - 10.1080/00927870902922968

M3 - Article

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SN - 0092-7872

VL - 38

SP - 1385

EP - 1400

JO - Communications in Algebra

JF - Communications in Algebra

IS - 4

ER -

On the prime ideal structure of Bhargava rings

Abstract

Keywords

ASJC Scopus subject areas

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