Difference between revisions of "Zero divisor"
From Encyclopedia of Mathematics
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''in a ring or a semi-group with zero element'' | ''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 | + | A non-zero element such that the product with some non-zero element is zero. An element $a$ is called a left (right) divisor of zero if $ab=0$ ($ba=0$) for at least one $b\neq0$. |
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| − | Let | + | Let $A$ be a ring and $M$ a left module over $A$. Then an element $a\neq0$ of $A$ is called a zero divisor in the module $M$ if there is an $m\in M$ such that $am=0$. |
Latest revision as of 12:22, 9 April 2014
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 $a$ is called a left (right) divisor of zero if $ab=0$ ($ba=0$) for at least one $b\neq0$.
Comments
Let $A$ be a ring and $M$ a left module over $A$. Then an element $a\neq0$ of $A$ is called a zero divisor in the module $M$ if there is an $m\in M$ such that $am=0$.
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