Zero divisor

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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 $b\neq0$.


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:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article