Acta Mathematica Hungarica
Volume/Issue:
Volume 102: Issue 4
A note on strongly π-regular rings
Author:
A. Chin University of Malaya Institute of Mathematical Sciences, Faculty of Science 50603 Kuala Lumpur Malaysia 50603 Kuala Lumpur Malaysia

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Pages:
337–342
Online Publication Date:
02 Nov 2004
Publication Date:
03 Mar 2004
Article Category:
Research Article
DOI:
https://doi.org/10.1023/b:amhu.0000024683.13344.cf
Keywords:
periodic; nilpotent; Jacobson radical; idempotent; regular; strongly ?-regular
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Abstract  

Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that xn=xn+1y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and xm=xn. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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