Some remarks on one-sided regularity

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.

Keywords

right (left) regular element / right (left) regular-duo ring / upper triangular matrix ring / right (left) Ore domain

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