semigroup love

# semigroup

## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• n. Mathematics A set for which there is a binary operation that is closed and associative.

• n. Any set for which there is a binary operation that is both closed and associative.

semi- +‎ group

## Examples

• A semigroup is a set together with an associative operation, called the multiplication of the semigroup and notated xy rather than f (x, y).

Algebra

• The final equation for the evolution at the ensemble level is of the quantum dynamical semigroup type and has a structure extremely similar to the final one of the GRW theory.

Collapse Theories

• X, whence the semigroup of all functions on a set X forms a monoid.

Algebra

• The semigroup of all nonempty words over a given alphabet has as a subsemigroup the words of even length; however the words of odd length do not form a subsemigroup because the concatenation of two odd-length words is not of odd length.

Algebra

• A commutative semigroup is a semigroup whose operation is commutative.

Algebra

• "Non-breaking error handling is just an applicative functor on a partially applied disjoint union type constructor with semigroup error elements so what's the big deal?"

developerFusion - content

• These considerations illustrate how the commonly used semigroup ansatz for time evolution of the unstable systems arises.