[[Ring|ring]]) over a
...\End{\textrm{End}}\End_L(\Ga)$ of the additive group scheme $\Ga/L$ is the ring of additive polynomials $f(x)\in L[x]$, i.e., of polynomials satisfying $f(
19 KB (3,204 words) - 20:11, 14 April 2012
''simplicial scheme, abstract simplicial complex''
...re is usually called an (abstract) simplicial complex; the term simplicial scheme would normally be understood to mean a simplicial object in the category of
11 KB (1,773 words) - 09:56, 13 February 2024
is a [[Chow ring|Chow ring]], or $ H ^ {. } X $
is the ring associated to the Grothendieck ring $ K ^ {0} ( X) $ (see [[#References|[2]]], [[#References|[7]]]). Let $
10 KB (1,385 words) - 03:10, 2 March 2022
...0 }$ exist? (The $5$-scheme $x$ is known as the deformation or lift of the scheme $X _ { 0 }$ over $5$.)
...rsal) deformation of a scheme $X _ { 0 }$ (i.e. a deformation $N$ over the scheme $X _ { 0 }$ such that for any other deformation $X \rightarrow S$ it is pos
40 KB (5,788 words) - 13:36, 17 October 2019
...ension]]) one, and "adding a point" $\infty$ to the corresponding [[Scheme|scheme]] $\operatorname {Spec}( \mathbf{Z})$ makes it look like a complete curve.
In higher dimension, given a regular projective flat scheme $X$ over $\mathbf{Z}$, one considers pairs $( Z , g )$ consisting of an alg
8 KB (1,219 words) - 21:00, 13 July 2020
be a scheme over a field
be a scheme and let
41 KB (5,916 words) - 11:24, 26 March 2023
is an associative algebra over a commutative ring $ K $
is the ring of integers, $ G $
19 KB (2,870 words) - 09:48, 26 March 2023
Any Boolean algebra is a [[Boolean ring|Boolean ring]] with a unit element with respect to the operations of "addition" ( $ +
any Boolean ring with a unit element can be considered as a Boolean algebra.
14 KB (2,077 words) - 21:17, 17 January 2021
...n $fg=0$ on $L$ implies that $f$ or $g$ is zero; in that case the quotient ring $K_L = K/I_L$ does not have divisors of zero (cf.
...o divisor]]) and is called the ring of polynomials on $L$ (here $K$ is the ring of all polynomials).
11 KB (1,916 words) - 00:44, 12 August 2019
of all unitary left modules over an arbitrary associative ring $ R $
with diagram scheme $ \mathfrak D $
10 KB (1,515 words) - 18:19, 31 March 2020
...functors on various categories of algebraic objects (modules over a given ring, sheaves, etc.).
...in of application of homological algebra is the category of modules over a ring. Most of the results known for modules may be applied to abelian categories
12 KB (1,885 words) - 23:48, 23 April 2017
...on [[localization of a category]], a generalisation of [[localization of a ring]]. The original impulse to develop the "derived" formalism came from the ne
...a single ''dualizing sheaf'' became apparent. In fact the [[Cohen-Macaulay ring]] condition, a weakening of non-singularity, corresponds to the existence o
15 KB (2,268 words) - 10:42, 5 March 2012
...ring of polynomials in a finite number of variables over a field or over a ring of integers any ideal is generated by a finite number of elements (has a fi
be a ring of polynomials over $ k $,
18 KB (2,720 words) - 19:17, 19 December 2019
...ring of polynomials in a finite number of variables over a field or over a ring of integers any ideal is generated by a finite number of elements (has a fi
Let $k$ be a field, let $k [ X _ { 1 } , \ldots , X _ { x } ]$ be a ring of polynomials over $k$, let $k$ be the algebraic closure of $k$, and let $
19 KB (2,744 words) - 13:36, 17 October 2019
be the [[field of fractions]] of a regular discretely-normed ring $ O $
then its minimal [[Néron model|Néron model]] is a smooth group scheme $ X \rightarrow \mathop{\rm Spec} O $,
6 KB (840 words) - 17:39, 16 July 2024
...G \rightarrow G$ one obtains a commutative algebra $4$ over a commutative ring $k$ with a homomorphism $\Delta : A \rightarrow A \otimes A$, called comult
...nor cocommutative. Fix $n \in N$ and $q \in k$, where $k$ is a commutative ring. Denote by $4$ the associative $k$-algebra with generators $x _ { i }$, $1
17 KB (2,598 words) - 13:44, 17 October 2019
[[Buchsbaum ring]] |
[[Difference scheme, variational]] |
15 KB (1,797 words) - 15:27, 6 May 2012
...ery such is axiomatizable by a single sentence and an "axiom of infinity" -scheme.
...matrix ring over an algebraically closed field; every superstable division ring is an algebraically closed field. G.L. Cherlin (middle of the 1970's) conje
11 KB (1,671 words) - 11:38, 22 December 2019
...ery such is axiomatizable by a single sentence and an "axiom of infinity" -scheme.
...matrix ring over an algebraically closed field; every superstable division ring is an algebraically closed field. G.L. Cherlin (middle of the 1970's) conje
11 KB (1,665 words) - 13:44, 17 October 2019
...s (this principle becomes a theorem if "space" is understood to be "affine scheme" or "compact topological space" , and "algebra" is understood to mean "C*-a
over a commutative ring $ k $
18 KB (2,674 words) - 19:09, 16 December 2019