finitely generated (English, adj)
expansion: finitely generated (not comparable)
Senses:
topics: algebra
category-theory
computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
glosses: 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:
Such that the functor operatorname Hom_( mathcal )C(X,·) preserves those filtered colimits of monomorphisms.
qualifier: most generally
tags: not-comparable
raw_tags: of an object X in a locally small category 𝒞 that admits filtered colimits of monomorphism
topics: algebra
mathematics
sciences
glosses: 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:
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.
qualifier: less generally; but still covering most cases outside pure category theory; less generally; but still covering most cases outside pure category theory
tags: not-comparable
raw_tags: of an object X in a concrete category
topics: algebra
mathematics
sciences
glosses: 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:
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.)
qualifier: module; ring; module; ring
tags: abstract
not-comparable
usually
raw_tags: of a group-like structure
topics: algebra
mathematics
sciences
glosses: 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:
Finitely generated as a (left) module over R.
qualifier: ring theory
tags: not-comparable
raw_tags: of a (left) ideal in a ring R
topics: algebra
mathematics
sciences
glosses: 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:
Equipped with an Alexandrov topology (i.e. one where the intersection of every family of open sets is open).
tags: not-comparable
raw_tags: of a space
Forms: