In mathematics, a finitely generated algebra (also called an algebra of finite type) is a commutative associative algebra A {\displaystyle A} over a field...

concepts of finitely generated, finitely presented and coherent modules coincide. A finitely generated module over a field is simply a finite-dimensional...

Finitely generated abelian group Finitely generated module Finitely generated ideal Finitely generated algebra Finitely generated space This disambiguation page...

term finite field. finite type An algebra over a ring is said to be of finite type if it is finitely generated as an algebra. finitely generated 1.  A...

a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In calculus and analysis, for example, σ-algebras are used...

a finite (hence finitely generated) abelian group. Any direct sum of finitely many finitely generated abelian groups is again a finitely generated abelian...

In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization...

basic operations such as sum or products of ideals. Ideals in a finitely generated algebra over a field (that is, a quotient of a polynomial ring over a...

In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination...

In abstract algebra, an associative algebra A {\displaystyle A} over a ring R {\displaystyle R} is called finite if it is finitely generated as an R {\displaystyle...

Hilbert's problems proposed in 1900, asks whether certain algebras are finitely generated. The setting is as follows: Assume that k is a field and let...

However, it is true that for finitely presented modules M over a commutative ring R (in particular if M is a finitely generated R-module and R is Noetherian)...

finitely generated by finitely many invariants of G (because if we are given any – possibly infinite – subset S that generates a finitely generated ideal...

finitely many elements a1, ..., an such that I = Ra1R + ... + RanR. 2.  A finitely generated ring is a ring that is finitely generated as Z-algebra....

finite group G acting on a finitely generated algebra R: since R is integral over RG, the Artin–Tate lemma implies RG is a finitely generated algebra...

to generate M if the smallest submonoid of M containing S is M. If there is a finite set that generates M, then M is said to be a finitely generated monoid...

finitely presented may refer to: finitely presented group finitely presented monoid finitely presented module finitely presented algebra finitely presented...

finitely generated. It is generated by the inverses of all the integers, but any finite number of these generators can be removed from the generating...

semigroup S is finitely generated if and only if its semigroup algebra C [ S ] {\displaystyle \mathbb {C} [S]} is a finitely generated algebra over C {\displaystyle...

in dimensions. A ring is called universally catenary if all finitely generated algebras over it are catenary rings. The word 'catenary' is derived from...

commutative algebra, introduced by Emmy Noether in 1926. It states that for any field k, and any finitely generated commutative k-algebra A, there exist...

every finitely generated field extension is separably generated; i.e., it admits a finite separating transcendence basis. An extension is algebraic if and...

f} is finite ( B {\displaystyle B} finitely generated A {\displaystyle A} -module) or of finite type ( B {\displaystyle B} finitely generated A {\displaystyle...

those that are spanned by a finite set are the finitely generated modules. Module homomorphisms between finitely generated free modules may be represented...

, is finitely generated if and only if α is an algebraic integer. The proof is analogous to that of the corresponding fact regarding algebraic numbers...

Affine algebra may refer to: Affine Lie algebra, a type of Kac–Moody algebras The Lie algebra of the affine group Finitely-generated algebra Affine Hecke...

dimension at most 1. Many of the modules over this algebra that occur in Iwasawa theory are finitely generated torsion modules. The structure of such modules...

makes Ai a finitely generated module over Bi (in other words, a finite Bi-algebra). One also says that X is finite over Y. In fact, f is finite if and only...

{\displaystyle S} is finite, [ S ] {\displaystyle [S]} is generally not finitely generated as an algebraic ideal. The radical differential ideal generated by S {\displaystyle...

a finite set. In other words, A {\displaystyle A} contains all but finitely many elements of X . {\displaystyle X.} If the complement is not finite, but...