Definition of Monoids. Meaning of Monoids. Synonyms of Monoids

- is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation...
- of free semigroups is called combinatorial semigroup theory. Free monoids (and monoids in general) are ****ociative, by definition; that is, they are written...
- is a topological monoid. A monoid object in the category of monoids (with the direct product of monoids) is just a commutative monoid. This follows easily...
- relations show that ba commutes with both a and b. Presentations of inverse monoids and semigroups can be defined in a similar way using a pair ( X ; T ) {\displaystyle...
- universal, in that all dependency-homomorphic (see below) monoids are in fact isomorphic. Trace monoids are commonly used to model concurrent com****tion, forming...
- identity element can be easily turned into a monoid by just adding an identity element. Consequently, monoids are studied in the theory of semigroups rather...
- In abstract algebra, a monoid ring is a ring constructed from a ring and a monoid, just as a group ring is constructed from a ring and a group. Let R be...
- group. This theorem generalizes straightforwardly to monoids: any monoid M is a transformation monoid of its underlying set, via the action given by left...
- language with syntactic monoid Z / 2 n Z {\displaystyle \mathbb {Z} /2^{n}\mathbb {Z} } . Trace monoids are examples of syntactic monoids. Marcel-Paul Schützenberger...
- binary operation on the affine monoid M {\displaystyle M} . Affine monoids are also torsion free. For an affine monoid M {\displaystyle M} , n x = n y...