Essential domains and two conjectures in dimension theory

M. Fontana; S. Kabbaj

doi:10.1090/S0002-9939-04-07502-1

Essential domains and two conjectures in dimension theory

M. Fontana^*, S. Kabbaj

^*Corresponding author for this work

Department of Mathematics

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

16 Scopus citations

Abstract

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.

Original language	English
Pages (from-to)	2529-2535
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	132
Issue number	9
DOIs	https://doi.org/10.1090/S0002-9939-04-07502-1
State	Published - Sep 2004

Keywords

Essential domain
Integer-valued polynomial ring
Jaffard domain
Kronecker function ring
Krull dimension
Krull domain
PVMD
Star operation
UFD
Valuative dimension

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-04-07502-1

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@article{f05a144244e6417ca2ec0813d4f94380,

title = "Essential domains and two conjectures in dimension theory",

abstract = "This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.",

keywords = "Essential domain, Integer-valued polynomial ring, Jaffard domain, Kronecker function ring, Krull dimension, Krull domain, PVMD, Star operation, UFD, Valuative dimension",

author = "M. Fontana and S. Kabbaj",

year = "2004",

month = sep,

doi = "10.1090/S0002-9939-04-07502-1",

language = "English",

volume = "132",

pages = "2529--2535",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

number = "9",

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TY - JOUR

T1 - Essential domains and two conjectures in dimension theory

AU - Fontana, M.

AU - Kabbaj, S.

PY - 2004/9

Y1 - 2004/9

N2 - This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.

AB - This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.

KW - Essential domain

KW - Integer-valued polynomial ring

KW - Jaffard domain

KW - Kronecker function ring

KW - Krull dimension

KW - Krull domain

KW - PVMD

KW - Star operation

KW - UFD

KW - Valuative dimension

UR - https://www.scopus.com/pages/publications/4344696824

U2 - 10.1090/S0002-9939-04-07502-1

DO - 10.1090/S0002-9939-04-07502-1

M3 - Article

AN - SCOPUS:4344696824

SN - 0002-9939

VL - 132

SP - 2529

EP - 2535

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 9

ER -

Essential domains and two conjectures in dimension theory

Abstract

Keywords

ASJC Scopus subject areas

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