Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 4: 833 - 847

DOI: https://doi.org/10.1007/s11464-018-0711-2

RESEARCH ARTICLE

Some remarks on one-sided regularity

  • Tai Keun KWAK , 1 ,
  • Yang LEE 2 ,
  • Young Joo SEO 3
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  • 1. Department of Mathematics, Daejin University, Pocheon 11159, Korea
  • 2. Institute of Basic Science, Daejin University, Pocheon 11159, Korea
  • 3. Department of Mathematics, Hanyang University, Seoul 04763, Korea

Received date: 30 Mar 2017

Accepted date: 04 Jul 2018

Published date: 14 Aug 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

A ring is said to be right (resp., left) regular-duo if every right (resp., left) regular element is regular. The structure of one-sided regular elements is studied in various kinds of rings, especially, upper triangular matrix rings over one-sided Ore domains. We study the structure of (one-sided) regular-duo rings, and the relations between one-sided regular-duo rings and related ring theoretic properties.

Key words： right (left) regular element; right (left) regular-duo ring; upper triangular matrix ring; right (left) Ore domain

Cite this article

Tai Keun KWAK , Yang LEE , Young Joo SEO . Some remarks on one-sided regularity[J]. Frontiers of Mathematics in China, 2018 , 13(4) : 833 -847 . DOI: 10.1007/s11464-018-0711-2

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