The failure of the Artin-Rees property for the Jacobson radical in prime Noetherian rings

A. Braun; C. R. Hajarnavis

doi:10.1016/j.jalgebra.2011.09.023

The failure of the Artin-Rees property for the Jacobson radical in prime Noetherian rings

A. Braun
, C. R. Hajarnavis

Department of Mathematics

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

Abstract

We provide an example of a prime Noetherian ring whose Jacobson radical fails to satisfy the Artin-Rees (AR) property on either side. The ring constructed is a finite module over its Noetherian centre. This settles a longstanding question.

Original language	English
Pages (from-to)	294-301
Number of pages	8
Journal	Journal of Algebra
Volume	348
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.09.023
State	Published - 15 Dec 2011

Keywords

Artin-Rees property
Noetherian rings
Non-commutative ring theory
PI rings

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2011.09.023

Cite this

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title = "The failure of the Artin-Rees property for the Jacobson radical in prime Noetherian rings",

abstract = "We provide an example of a prime Noetherian ring whose Jacobson radical fails to satisfy the Artin-Rees (AR) property on either side. The ring constructed is a finite module over its Noetherian centre. This settles a longstanding question.",

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AB - We provide an example of a prime Noetherian ring whose Jacobson radical fails to satisfy the Artin-Rees (AR) property on either side. The ring constructed is a finite module over its Noetherian centre. This settles a longstanding question.

KW - Artin-Rees property

KW - Noetherian rings

KW - Non-commutative ring theory

KW - PI rings

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DO - 10.1016/j.jalgebra.2011.09.023

M3 - Article

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VL - 348

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JO - Journal of Algebra

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The failure of the Artin-Rees property for the Jacobson radical in prime Noetherian rings

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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