Zero divisor
From Encyclopedia of Mathematics
in a ring or a semi-group with zero element
A non-zero element such that the product with some non-zero element is zero. An element 
is called a left (right) divisor of zero if 
(
) for at least one 
.
Comments
Let 
be a ring and 
a left module over 
. Then an element 
of 
is called a zero divisor in the module 
if there is an 
such that 
.
How to Cite This Entry:
Zero divisor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Zero_divisor&oldid=17967
Zero divisor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Zero_divisor&oldid=17967
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article