Bhargava rings over subsets

I. Al-Rasasi; L. Izelgue

doi:10.1007/978-3-319-74195-6_2

Bhargava rings over subsets

I. Al-Rasasi
, L. Izelgue^*

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

Let D be an integral domain with quotient field K and let E be any nonempty subset of K. The Bhargava ring over E at x∈ D is defined by Bx(E,D):={f∈K[X]∣f(xX+e)∈D[X],∀e∈E}. This ring is a subring of the ring of integer-valued polynomials over E. This paper studies B_x(E, D) for an arbitrary domain D. we provide information about its localizations and transfer properties, describe its prime ideal structure, and calculate its Krull and valuative dimensions.

Original language	English
Title of host publication	Homological and Combinatorial Methods in Algebra - SAA 4, Ardabil, Iran, August 2016
Editors	Ayman Badawi, Mohammad Reza Vedadi, Ahmad Yousefian Darani, Siamak Yassemi
Publisher	Springer New York LLC
Pages	9-26
Number of pages	18
ISBN (Print)	9783319741949
DOIs	https://doi.org/10.1007/978-3-319-74195-6_2
State	Published - 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	228
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2018.

Keywords

Bhargava ring
Integer-valued polynomial
Krull dimension
Localization residue field
Prime ideal
Valuative dimension

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-74195-6_2

Cite this

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title = "Bhargava rings over subsets",

abstract = "Let D be an integral domain with quotient field K and let E be any nonempty subset of K. The Bhargava ring over E at x∈ D is defined by Bx(E,D):=\{f∈K[X]∣f(xX+e)∈D[X],∀e∈E\}. This ring is a subring of the ring of integer-valued polynomials over E. This paper studies Bx(E, D) for an arbitrary domain D. we provide information about its localizations and transfer properties, describe its prime ideal structure, and calculate its Krull and valuative dimensions.",

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

author = "I. Al-Rasasi and L. Izelgue",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2018.",

year = "2018",

doi = "10.1007/978-3-319-74195-6\_2",

language = "English",

isbn = "9783319741949",

series = "Springer Proceedings in Mathematics and Statistics",

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pages = "9--26",

editor = "Ayman Badawi and Vedadi, \{Mohammad Reza\} and \{Yousefian Darani\}, Ahmad and Siamak Yassemi",

booktitle = "Homological and Combinatorial Methods in Algebra - SAA 4, Ardabil, Iran, August 2016",

}

Bhargava rings over subsets. / Al-Rasasi, I.; Izelgue, L.
Homological and Combinatorial Methods in Algebra - SAA 4, Ardabil, Iran, August 2016. ed. / Ayman Badawi; Mohammad Reza Vedadi; Ahmad Yousefian Darani; Siamak Yassemi. Springer New York LLC, 2018. p. 9-26 (Springer Proceedings in Mathematics and Statistics; Vol. 228).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Bhargava rings over subsets

AU - Al-Rasasi, I.

AU - Izelgue, L.

N1 - Publisher Copyright: © Springer International Publishing AG 2018.

PY - 2018

Y1 - 2018

N2 - Let D be an integral domain with quotient field K and let E be any nonempty subset of K. The Bhargava ring over E at x∈ D is defined by Bx(E,D):={f∈K[X]∣f(xX+e)∈D[X],∀e∈E}. This ring is a subring of the ring of integer-valued polynomials over E. This paper studies Bx(E, D) for an arbitrary domain D. we provide information about its localizations and transfer properties, describe its prime ideal structure, and calculate its Krull and valuative dimensions.

AB - Let D be an integral domain with quotient field K and let E be any nonempty subset of K. The Bhargava ring over E at x∈ D is defined by Bx(E,D):={f∈K[X]∣f(xX+e)∈D[X],∀e∈E}. This ring is a subring of the ring of integer-valued polynomials over E. This paper studies Bx(E, D) for an arbitrary domain D. we provide information about its localizations and transfer properties, describe its prime ideal structure, and calculate its Krull and valuative dimensions.

KW - Bhargava ring

KW - Integer-valued polynomial

KW - Krull dimension

KW - Localization residue field

KW - Prime ideal

KW - Valuative dimension

UR - https://www.scopus.com/pages/publications/85043570230

U2 - 10.1007/978-3-319-74195-6_2

DO - 10.1007/978-3-319-74195-6_2

M3 - Conference contribution

AN - SCOPUS:85043570230

SN - 9783319741949

T3 - Springer Proceedings in Mathematics and Statistics

SP - 9

EP - 26

BT - Homological and Combinatorial Methods in Algebra - SAA 4, Ardabil, Iran, August 2016

A2 - Badawi, Ayman

A2 - Vedadi, Mohammad Reza

A2 - Yousefian Darani, Ahmad

A2 - Yassemi, Siamak

PB - Springer New York LLC

ER -

Bhargava rings over subsets

Abstract

Publication series

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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