different between closed vs semigroup

English

Pronunciation

• (Received Pronunciation) IPA^(key): /kl??zd/
• (General American) IPA^(key): /klo?zd/
• Rhymes: -??zd

Adjective

closed (not comparable)

1. Sealed, made inaccessible or impassable; not open.
2. (of a store or business) Not operating or conducting trade.
3. Not public.

4. (topology, of a set) Having an open complement.
5. (mathematics, of a set) Such that its image under the specified operation is contained in it.

6. (mathematics, logic, of a formula) Lacking a free variable.
7. (graph theory, of a walk) Whose first and last vertices are the same, forming a closed loop.
8. (phonology) Formed by closing the mouth and nose passages completely, like the consonants /t/, /d/, and /p/.
9. (phonology) Having the sound cut off sharply by a following consonant, like the /?/ in pin.

Synonyms

• shut

Antonyms

• (also phonetics (of vowels, syllables)): open

Derived terms

• a closed mouth catches no flies
• a closed mouth gathers no feet

Translations

See also

• close

Verb

closed

1. simple past tense and past participle of close

Anagrams

• Dolces, codels, codles, dolces

Welsh

Pronunciation

• IPA^(key): /?kl?s?d/

Noun

closed m (plural closedau)

1. Alternative form of closet

Mutation

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)

1. (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.

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