...y subgroup of finite index in $\def\O{\mathcal{O}}G_\O$, where $\O$ is the ring of integers in an algebraic number field $k$ (cf.
[[Algebraic number theory|Algebraic number theory]]) and $G$ is a connected
4 KB (613 words) - 21:48, 5 March 2012
''Associative rings and algebras'' are
rings and algebras with an associative multiplication, i.e., sets with
11 KB (1,726 words) - 20:09, 15 December 2020
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A [[Prime ideal|prime ideal]] in a [[Dedekind ring|Dedekind ring]] $ A $
3 KB (473 words) - 08:09, 6 June 2020
...bf{Z}_p$ of $p$-adic integers is a pro-$p$-group. In Galois theory pro-$p$-groups appear as [[Galois group]]s of $p$-extensions of fields.
...roperties: 1) $G$ is the smallest closed subgroup of $G$ generated by $E$; and 2) any neighbourhood of the identity of $G$ contains almost-all (i.e. all e
3 KB (535 words) - 19:45, 21 October 2017
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over the integral group ring $ \mathbf Z [ H ] $(
2 KB (302 words) - 08:01, 6 June 2020
Algebras introduced by B.Yu. Weisfeiler and A.A. Leman [[#References|[a9]]] and initially studied by representatives of the Soviet school of algebraic comb
A cellular algebra $W$ of order $n$ and rank $r$ is a matrix subalgebra of the full matrix algebra $\mathbf{C}^{n \
7 KB (1,000 words) - 16:48, 14 January 2021
[[Category:Number theory]]
An idele (also: idèle) is an invertible element of the ring of
4 KB (757 words) - 21:21, 22 November 2014
...e ring $R$ that is a topological space in which the operations of addition and multiplication, as well as the mapping $R\times A\to A$ ($(r,a)\to ra$), ar
...ctures, i.e. groups, semi-groups, rings, lattices, vector spaces, modules, and others, equipped with topologies in which the algebraic operations consider
9 KB (1,142 words) - 17:15, 15 November 2023
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and $ U _ {t} $
5 KB (837 words) - 08:04, 6 June 2020
$#C+1 = 44 : ~/encyclopedia/old_files/data/R082/R.0802430 Ring with divided powers
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4 KB (663 words) - 08:28, 20 January 2024
...encyclopedia/old_files/data/R081/R.0801470 Representation of the symmetric groups
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18 KB (2,500 words) - 13:04, 18 February 2022
...r]] from $\Gamma$ to the [[category]] of $R$-modules, for some commutative ring $R$ (cf. also [[Module]]). Taking morphisms to be natural transformations,
...orbits $G/H$ and $G$-mappings between them. $\mathbf{Z}$-modules (Abelian groups) over $\mathcal{O}_G$ play the role of the coefficients in Bredon's ($\math
3 KB (473 words) - 18:52, 28 October 2016
...n, i.e. to use the plus sign ($+$) for that operation, called "addition", and the zero sign for the neutral element, named zero (in multiplicative notati
...a group in which all finitely generated subgroups are cyclic. Finally, the groups of type $p^\infty$ (or the [[quasi-cyclic group]]s $\mathbf Z_{p^\infty}$),
11 KB (1,810 words) - 22:12, 29 August 2015
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and $ x + \infty = \infty + x = \infty $
14 KB (2,135 words) - 08:27, 6 June 2020
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be a ring with unit and $ M $
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...oups [[#References|[4]]], [[#References|[5]]], and in the theory of formal groups [[#References|[6]]]. Let $ A $
be an associative, commutative ring with unit element. Witt vectors with components in $ A $
17 KB (2,502 words) - 17:25, 22 December 2019
[[Category:Ergodic theory]]
A continuous flow in [[Ergodic theory|ergodic theory]] is a family $\{T^t\}$ (where $t$ ranges over the real axis $\R$) of autom
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...{{Cite|Ma}}, {{Cite|Se}}, {{Cite|SaVa}}, {{Cite|GrSe}}) or as automorphism groups of large objects ({{Cite|HaMc}}; for example, the group of all bijections o
...logical space is completely determined by a certain perfect, locally free, and hence acyclic, group {{Cite|BeCa}}.
6 KB (873 words) - 08:18, 18 February 2022
...erous applications in algebraic geometry, class field theory and cobordism theory.
and field of residues $ k $ ,
17 KB (2,537 words) - 22:38, 15 December 2019
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and an Abelian group $ G $.
16 KB (2,386 words) - 16:47, 20 January 2024