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and such that all its local homology groups (cf. [[Local homology|Local homology]]) $ H _ {p} ^ {x} $
9 KB (1,445 words) - 22:10, 5 June 2020
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be an associative ring with unit element. A sequence of elements $ ( a _ {1} \dots a _ {n} ) $
7 KB (1,046 words) - 08:22, 6 June 2020
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of an algebra (group, ring, etc.) $ A $
2 KB (242 words) - 16:40, 31 March 2020
...ariski topology), is not a topological group with respect to this topology and therefore is not a compact group.
The following groups are two important classes of compact groups.
8 KB (1,148 words) - 13:36, 17 October 2019
.... also [[Pro-p group|Pro-$p$-group]]; [[Cohomology of groups|Cohomology of groups]]). The original proof appeared in [[#References|[a7]]], a proof in the con
...extbf{Z}/p\to\textbf{Z}/p^2\to\textbf{Z}/p\to 0$ (see [[#References|[a9]]] and [[Cohomology operation|Cohomology operation]]). Note that for $p=2$ this is
6 KB (868 words) - 22:16, 5 February 2021
...bilinear form $\Phi$ on a left $K$-module $E$, where $K$ is a commutative ring (cf.
[[Classical group|Classical group]]). In the case when $E=K^{2m}$ and the matrix of $\Phi$ with respect to the canonical basis $\{e_i\}$ of $E$ h
6 KB (1,078 words) - 14:22, 3 November 2013
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and $ F _ {2} $
4 KB (558 words) - 16:18, 6 June 2020
|[[Method of extensions and restrictions]]
|[[Noetherian ring]]
5 KB (641 words) - 11:27, 6 June 2020
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be a [[Scheme|scheme]] and let $ p $
6 KB (885 words) - 08:04, 6 June 2020
$#C+1 = 244 : ~/encyclopedia/old_files/data/C023/C.0203130 Cohomology of groups
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16 KB (2,427 words) - 09:48, 26 March 2023
...$A$ is called a left polygon over a monoid $R$ if for any $\lambda \in R$ and $a \in A$ the product $\lambda a \in A$ is defined, such that
and
6 KB (1,055 words) - 05:59, 22 April 2023
[[Chow ring|Chow ring]] $A(G_{n,m})$, and for $k=\C$ — a basis for the homology group $H_*(G_{n,m},\Z)$.
...operties. Hilbert's 15th problem concerns a foundation for the enumeration theory developed by Schubert (see
3 KB (391 words) - 16:26, 9 December 2023
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...eld (cf. also [[Algebraic number|Algebraic number]]; [[Field|Field]]) with ring of integers $ R $
4 KB (600 words) - 17:32, 5 June 2020
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the structure of a module over the integer group ring $ \mathbf Z (J ^ {a} ) $
12 KB (1,694 words) - 06:42, 26 March 2023
...a monoid (a semi-group with a unit element) and an inner automorphism of a ring (associative with a unit element), which are introduced in a similar way us
Let $\mathfrak{g}$ be a [[Lie algebra]] and $x \in \mathfrak{g}$ an element of $\mathfrak{g}$ for which $\mathrm{ad}(x)
2 KB (338 words) - 21:00, 29 November 2014
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...a generalized manifold) with coefficients in a locally constant system of groups (modules) $ {\mathcal G} $,
8 KB (1,257 words) - 05:06, 7 March 2022
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...operations, that is, addition, multiplication and transitions to negative and inverse elements (the latter is defined only on the set of non-zero element
5 KB (680 words) - 22:17, 5 June 2020
A category $\mathfrak C$ in which for any two objects $X$ and $Y$ an Abelian group structure is defined on the set of morphisms $\Hom_{\m
...of a category]]) as well as the product $X\times Y$ of any two objects $X$ and $Y$.
3 KB (490 words) - 23:53, 10 December 2018
The theory that studies arithmetic properties of linear algebraic groups (cf.
...he principal objects of study in the arithmetic theory of linear algebraic groups are arithmetic subgroups of an algebraic group $G$ (see
11 KB (1,671 words) - 18:19, 24 May 2019
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A [[Morphism|morphism]] $\mu : M \rightarrow P$ of groups together with an action of the [[Group|group]] $P$ on the group $M$ satisfy
9 KB (1,326 words) - 16:58, 1 July 2020