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=34139
Annihilator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Annihilator&oldid=34139
This article was adapted from an original article by K.A. Zhevlakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article