Noetherian domains which admit only finitely many star operations

Evan Houston; Abdeslam Mimouni; Mi Hee Park

doi:10.1016/j.jalgebra.2012.05.015

Noetherian domains which admit only finitely many star operations

Evan Houston^*
, Abdeslam Mimouni
, Mi Hee Park

^*Corresponding author for this work

Department of Mathematics

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

23 Scopus citations

Abstract

In this paper, we study Noetherian domains which admit only finitely many star operations. We show that such domains (which are not fields) must have Krull dimension one, and we effectively reduce to the local case. For a one-dimensional local Noetherian domain (R, M), M nonprincipal, M ^-1 is an overring of R, and M ^-1/M is naturally an R/M-vector space. We succeed in counting the number of star operations on R in several cases when dim _R/MM ^-1/M=3.

Original language	English
Pages (from-to)	78-93
Number of pages	16
Journal	Journal of Algebra
Volume	366
DOIs	https://doi.org/10.1016/j.jalgebra.2012.05.015
State	Published - 15 Sep 2012

Keywords

Divisorial ideal
Noetherian domain
Star operation

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2012.05.015

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title = "Noetherian domains which admit only finitely many star operations",

abstract = "In this paper, we study Noetherian domains which admit only finitely many star operations. We show that such domains (which are not fields) must have Krull dimension one, and we effectively reduce to the local case. For a one-dimensional local Noetherian domain (R, M), M nonprincipal, M -1 is an overring of R, and M -1/M is naturally an R/M-vector space. We succeed in counting the number of star operations on R in several cases when dim R/MM -1/M=3.",

keywords = "Divisorial ideal, Noetherian domain, Star operation",

author = "Evan Houston and Abdeslam Mimouni and Park, \{Mi Hee\}",

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T1 - Noetherian domains which admit only finitely many star operations

AU - Houston, Evan

AU - Mimouni, Abdeslam

AU - Park, Mi Hee

PY - 2012/9/15

Y1 - 2012/9/15

N2 - In this paper, we study Noetherian domains which admit only finitely many star operations. We show that such domains (which are not fields) must have Krull dimension one, and we effectively reduce to the local case. For a one-dimensional local Noetherian domain (R, M), M nonprincipal, M -1 is an overring of R, and M -1/M is naturally an R/M-vector space. We succeed in counting the number of star operations on R in several cases when dim R/MM -1/M=3.

AB - In this paper, we study Noetherian domains which admit only finitely many star operations. We show that such domains (which are not fields) must have Krull dimension one, and we effectively reduce to the local case. For a one-dimensional local Noetherian domain (R, M), M nonprincipal, M -1 is an overring of R, and M -1/M is naturally an R/M-vector space. We succeed in counting the number of star operations on R in several cases when dim R/MM -1/M=3.

KW - Divisorial ideal

KW - Noetherian domain

KW - Star operation

UR - https://www.scopus.com/pages/publications/84861991765

U2 - 10.1016/j.jalgebra.2012.05.015

DO - 10.1016/j.jalgebra.2012.05.015

M3 - Article

AN - SCOPUS:84861991765

SN - 0021-8693

VL - 366

SP - 78

EP - 93

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Noetherian domains which admit only finitely many star operations

Abstract

Keywords

ASJC Scopus subject areas

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