Mathematical Structures and Commutativity
- A commutative semigroup is a set endowed with a total, associative and commutative operation.
- If the operation additionally has an identity element, we have a commutative monoid
- An abelian group, or commutative group is a group whose group operation is commutative.
- A commutative ring is a ring whose multiplication is commutative. (Addition in a ring is always commutative.)
- In a field both addition and multiplication are commutative.
Read more about this topic: Commutative Property
Famous quotes containing the words mathematical and/or structures:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“The American who has been confined, in his own country, to the sight of buildings designed after foreign models, is surprised on entering York Minster or St. Peter’s at Rome, by the feeling that these structures are imitations also,—faint copies of an invisible archetype.”
—Ralph Waldo Emerson (1803–1882)