monoid
Speech parts
1. monoid - Noun
2. monoid - Adjective
Meaning
monoid (plural monoids)
(mathematics) A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
monoid (not comparable)
(prosody) Containing only one kind of metrical foot.
Phrases with the word
Anagrams
Examples
Alternatively one can observe that the functor that for each group takes the underlying monoid (ignoring inverses) has a left adjoint.
By definition, a ring is a monoid object in the category of abelian groups ; thus, an associative algebra is obtained by replacing the category of abelian groups with the category of modules.
Category theoretical description main Every ring can be thought of as a monoid in Ab, the category of abelian groups (thought of as a monoidal category under the tensor product of -modules ).
Being lattices, Heyting algebras and Boolean algebras are endowed with these monoid structures.
A transformation semigroup can be made into an operator monoid by adjoining the identity transformation.
A small category with a single object is the same thing as a monoid : the morphisms of a one-object category can be thought of as elements of the monoid, and composition in the category is thought of as the monoid operation.