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| Title of object: |
commutative |
| Canonical Name: |
Commutative |
| Type: |
Definition |
| Created on: |
2002-02-18 21:51:51 |
| Modified on: |
2005-02-18 08:18:43 |
| Classification: |
msc:20-00 |
| Defines: |
non-commutative |
| Synonyms: |
commutative=commutativity |
Revision comment (for changes between this and next version):
| Changes for correction #13180 ('law'). |
Preamble:
\usepackage{amssymb}
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Content:
Let $(S,\phi)$ be a set with binary operation $\phi$. $\phi$ is said to be \emph{commutative} if
$$ \phi(a,b) = \phi(b,a)$$
for all $a,b \in S$.
Some operations which are commutative are addition over the integers, multiplication over the integers, addition over $n \times n$ matrices, and multiplication over the reals.
An example of a non-commutative operation is multiplication over $n \times n$ matrices. |
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