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