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
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The set
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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
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