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zero divisor

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

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.

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.

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

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

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