Definitions from Wiktionary (finitely generated)
▸ adjective: (algebra) In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:
▸ adjective: (most generally, category theory, of an object X in a locally small category ๐ that admits filtered colimits of monomorphism) Such that the functor operatorname Hom_( mathcal )C(X,ยท) preserves those filtered colimits of monomorphisms.
▸ adjective: (less generally, but still covering most cases outside pure category theory, of an object X in a concrete category) Being a quotient object of a free object over a finite set, i.e. being the target of a regular epimorphism from an object which is free on a finite set.
▸ adjective: (abstract algebra, of a group-like structure: a group, module, ring, monoid, etc.) Having a finite set of generators, i.e. having a finite set of elements from which all other elements can be created in finitely many steps under the permitted operations (viz. the group operation for groups, addition and scalar multiplication for modules, addition and multiplication for rings, etc.)
▸ adjective: (ring theory, of a (left) ideal in a ring R) Finitely generated as a (left) module over R.
▸ adjective: (of a space) Equipped with an Alexandrov topology (i.e. one where the intersection of every family of open sets is open).
Finitely generated group,
Finitely generated module,
Finitely generated abelian group,
Structure theorem for finitely generated modules over a principal ideal domain,
Finitely generated algebra,
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▸ adjective: (algebra) In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:
▸ adjective: (most generally, category theory, of an object X in a locally small category ๐ that admits filtered colimits of monomorphism) Such that the functor operatorname Hom_( mathcal )C(X,ยท) preserves those filtered colimits of monomorphisms.
▸ adjective: (less generally, but still covering most cases outside pure category theory, of an object X in a concrete category) Being a quotient object of a free object over a finite set, i.e. being the target of a regular epimorphism from an object which is free on a finite set.
▸ adjective: (abstract algebra, of a group-like structure: a group, module, ring, monoid, etc.) Having a finite set of generators, i.e. having a finite set of elements from which all other elements can be created in finitely many steps under the permitted operations (viz. the group operation for groups, addition and scalar multiplication for modules, addition and multiplication for rings, etc.)
▸ adjective: (ring theory, of a (left) ideal in a ring R) Finitely generated as a (left) module over R.
▸ adjective: (of a space) Equipped with an Alexandrov topology (i.e. one where the intersection of every family of open sets is open).
Phrases:
▸ Words similar to finitely generated
▸ Usage examples for finitely generated
▸ Idioms related to finitely generated
▸ Wikipedia articles (New!)
▸ Popular nouns described by finitely generated
▸ Words that often appear near finitely generated
▸ Rhymes of finitely generated
▸ Invented words related to finitely generated