Module scirust::algebra::structure::monoid

Defines the monoid algebraic structure.

A monoid is an algebraic structure with a single associative binary operation and an identity element. Monoids are studied in semigroup theory as they are semigroups with identity.

A commutative monoid is a monoid whose binary operation is commutative.

We define four kinds of monoids.

• Monoid with an addition operation with partial equivalence
• Monoid with an addition operation with full equivalence
• Monoid with a multiplication operation with partial equivalence
• Monoid with a multiplication operation with full equivalence

References:

• http://en.wikipedia.org/wiki/Algebraic_structure
• http://en.wikipedia.org/wiki/Monoid

Traits

CommutativeMonoidAdd	Commutative monoid with an addition operation with full equivalence
CommutativeMonoidAddPartial	Commutative monoid with an addition operation with partial equivalence
CommutativeMonoidMul	Commutative monoid with a multiplication operation with full equivalence
CommutativeMonoidMulPartial	Commutative monoid with a multiplication operation with partial equivalence
MonoidAdd	Monoid with an addition operation with full equivalence
MonoidAddPartial	Monoid with an addition operation with partial equivalence
MonoidMul	Monoid with a multiplication operation with full equivalence
MonoidMulPartial	Monoid with a multiplication operation with partial equivalence