# zero divisor

## Primary tabs

Defines:
left zero divisor, right zero divisor, regular element
Type of Math Object:
Definition
Major Section:
Reference

## Mathematics Subject Classification

13G05 no label found

## Comments

### regular element

There are now possibly 2 different definitions of a regular element of an element of a ring and they are not equivalent. First an element that is neither a left zero divisor nor right zero divisor and secondly p is regular in a ring if there exists s in R such that p = psp.

### Re: regular element

There are several mathematicians in whose books the second definition of regular is used namely : I. Herstein in Noncommutative Rings and N. McCoy in the Theory of Rings.

### Re: regular element

Change the comment about matjematicians to N. McCoy in the Theory of Rings.

### Re: regular element

Change the comment about mathematicians to N. McCoy in the Theory of Rings and Seth Warner in Modern Algebra about regular rings.