# Annihilator

From Encyclopedia of Mathematics

*left, of a set in *

The set of all elements in such that . Here is a ring or a semi-group (or, generally, a groupoid) with a zero. The right annihilator of a set in is defined in a similar manner as the set

The set

is the two-sided annihilator of . In an associative ring (or semi-group) the left annihilator of an arbitrary set is a left ideal, and if is a left ideal of , then is a two-sided ideal of ; in the non-associative case these statements are usually not true.

**How to Cite This Entry:**

Annihilator.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Annihilator&oldid=17045

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