different between semigroup vs monoid
semigroup
English
Etymology
From semi- +? group, reflecting the fact that not all the conditions required for a group are required for a semigroup. (Specifically, the requirements for the existence of identity and inverse elements are omitted.)
Noun
semigroup (plural semigroups)
- (mathematics) Any set for which there is a binary operation that is closed and associative.
- 1961, Alfred Hoblitzelle Clifford, G. B. Preston, The Algebraic Theory of Semigroups (page 70)
- If a semigroup S contains a zeroid, then every left zeroid is also a right zeroid, and vice versa, and the set K of all the zeroids of S is the kernel of S.
- 1988, A. Ya A?zenshtat, Boris M. Schein (translator), On Ideals of Semigroups of Endomorphisms, Ben Silver (editor), Nineteen Papers on Algebraic Semigroups, American Mathematical Society Translations, Series 2, Volume 139, page 11,
- It follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism semigroups.
- 2012, Jorge Almeida, Benjamin Steinberg, Syntactic and Global Subgroup Theory: A Synthesis Approach, Jean-Camille Birget, Stuart Margolis, John Meakin, Mark V. Sapir (editors), Algorithmic Problems in Groups and Semigroups, page 5,
- If one considers the variety of semigroups, one has the binary operation of multiplication defined on every semigroup.
- 1961, Alfred Hoblitzelle Clifford, G. B. Preston, The Algebraic Theory of Semigroups (page 70)
Hypernyms
- (set for which a closed associative binary operation is defined): magma
Hyponyms
- (set for which a closed associative binary operation is defined): group, monoid
Derived terms
- semigroup homomorphism
Translations
semigroup From the web:
monoid
English
Etymology
mono- +? -oid
Noun
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.
Hypernyms
- category
- semigroup
Hyponyms
Derived terms
Translations
See also
Adjective
monoid (not comparable)
- (prosody) Containing only one kind of metrical foot.
References
- monoid on Wikipedia.Wikipedia
Anagrams
- domino
Czech
Noun
monoid m
- monoid
Further reading
- monoid in Kartotéka Novo?eského lexikálního archivu
Serbo-Croatian
Noun
monoid m (Cyrillic spelling ??????)
- monoid
monoid From the web:
- what is monoid group
- what is monoid in discrete mathematics
- what is monoid in scala
- what is monoid example
- what does monoid mean
- what is monoidal category
- what is monoid in sets
- what is monoid groupoid
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