Absorbing element: Difference between revisions
Jump to navigation
Jump to search
imported>Richard Pinch (new entry, just a stub) |
imported>Richard Pinch (Moved See also to Related) |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{subpages}} | |||
In [[algebra]], an '''absorbing element''' or a '''zero element''' for a [[binary operation]] has a property similar to that of [[multiplication]] by [[zero]]. | In [[algebra]], an '''absorbing element''' or a '''zero element''' for a [[binary operation]] has a property similar to that of [[multiplication]] by [[zero]]. | ||
| Line 10: | Line 11: | ||
* 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. | |||
* [[ | |||
Latest revision as of 15:21, 21 December 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.