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...
- binary operation on the affine monoid M{\displaystyle M}. Affine monoids are also torsion free. For an affine monoid M{\displaystyle M}, nx=ny{\displaystyle...
- monoids were first presented by M.W. Shields. History monoids are isomorphic to trace monoids (free partially commutative monoids) and to the monoid of...
- 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...
- 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...
- 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...
- language with syntactic monoid Z/2nZ{\displaystyle \mathbb {Z} /2^{n}\mathbb {Z} }. Trace monoids are examples of syntactic monoids. Marcel-Paul Schützenberger...
- the trace monoid. The trace monoid is universal, in that all dependency-homomorphic (see below) monoids are in fact isomorphic. Trace monoids are commonly...