Absorbing element: Difference between revisions
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* The zero (additive identity element) of a [[ring (mathematics)|ring]] is an absorbing element for the ring multiplication. | * The zero (additive identity element) of a [[ring (mathematics)|ring]] is an absorbing element for the ring multiplication. | ||
* The [[zero matrix]] is the absorbing element for [[matrix multiplication]]. | * The [[zero matrix]] is the absorbing element for [[matrix multiplication]]. | ||
* The [[empty set]] is the absorbing element for [[intersection]] of sets. | |||
==See also== | ==See also== | ||
* [[Zero element]] | * [[Zero element]] | ||
Revision as of 16:02, 7 November 2008
In algebra, an absorbing element or a zero element for a binary operation has a property similar to that of multiplication by zero.
Formally, let be a binary operation on a set X. An element O of X is absorbing for if
holds for all x in X. An absorbing element, if it exists, is unique.
Examples
- The zero (additive identity element) of a ring is an absorbing element for the ring multiplication.
- The zero matrix is the absorbing element for matrix multiplication.
- The empty set is the absorbing element for intersection of sets.