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searching for Finitely generated algebra 13 found (32 total)

alternate case: finitely generated algebra

Goldman domain (635 words) [view diff] exact match in snippet view article find links to article

G-domain is an integral domain A whose field of fractions is a finitely generated algebra over A. They are named after Oscar Goldman. An overring (i.e.

Locally finite variety (274 words) [view diff] exact match in snippet view article find links to article

set of identities. One calls a variety locally finite if every finitely generated algebra has finite cardinality, or equivalently, if every finitely generated

Jacobson ring (829 words) [view diff] exact match in snippet view article find links to article

prime ideals. Any finitely generated algebra over a Jacobson ring is a Jacobson ring. In particular, any finitely generated algebra over a field or the

Gordan's lemma (1,251 words) [view diff] exact match in snippet view article find links to article

semigroup algebra C [ S ] {\displaystyle \mathbb {C} [S]} is a finitely generated algebra over C {\displaystyle \mathbb {C} } . To prove Gordan's lemma

Gelfand–Kirillov dimension (332 words) [view diff] exact match in snippet view article find links to article

x_{n}]} Is n. (Warfield) For any real number r ≥ 2, there exists a finitely generated algebra whose GK dimension is r. Given a right module M over the Weyl

G-ring (461 words) [view diff] exact match in snippet view article find links to article

not G-rings. Every localization of a G-ring is a G-ring Every finitely generated algebra over a G-ring is a G-ring. This is a theorem due to Grothendieck

Quillen–Lichtenbaum conjecture (535 words) [view diff] no match in snippet view article find links to article

The conjecture in Quillen's original form states that if A is a finitely-generated algebra over the integers and l is prime, then there is a spectral sequence

Catenary ring (777 words) [view diff] exact match in snippet view article find links to article

local rings) Any localization of a universally catenary ring Any finitely generated algebra over a universally catenary ring. It is delicate to construct

Krull dimension (1,745 words) [view diff] exact match in snippet view article find links to article

the same length. A ring is called universally catenary if any finitely generated algebra over it is catenary. Nagata gave an example of a Noetherian ring

Haboush's theorem (1,094 words) [view diff] exact match in snippet view article find links to article

reductive group (over an algebraically closed field) acts on a finitely generated algebra then the fixed subalgebra is also finitely generated. Haboush's

Integral element (5,304 words) [view diff] exact match in snippet view article find links to article

difficult question is on the finiteness of the integral closure of a finitely generated algebra. There are several known results. The integral closure of a Dedekind

Excellent ring (1,468 words) [view diff] exact match in snippet view article find links to article

excellent. Any localization of an excellent ring is excellent. Any finitely generated algebra over an excellent ring is excellent. This includes all polynomial

Locally nilpotent derivation (4,374 words) [view diff] exact match in snippet view article find links to article

g 1 , … , g n ] {\displaystyle A=k[g_{1},\dots ,g_{n}]} is a finitely generated algebra over a field of characteristic zero, then ker ⁡ ∂ {\displaystyle