...K $ . In this way an isomorphism is established between linear and matrix groups.
...[Field|field]]. Therefore henceforth (unless stated otherwise) only linear groups over a field will be considered.
16 KB (2,362 words) - 18:01, 12 December 2019
...eld is a Frobenius algebra. Every Frobenius algebra is a [[quasi-Frobenius ring]]. The converse is not true. The following properties of a finite-dimension
3) if $L$ is a left and $H$ is a right ideal of $R$, then (see [[Annihilator]])
2 KB (316 words) - 15:37, 5 February 2016
...algebra|Lie algebra]]; [[Alternative rings and algebras|Alternative rings and algebras]]; [[Jordan algebra|Jordan algebra]]; [[Mal'tsev algebra|Mal'tsev
...mple algebras that are far from associative — in the class of all algebras and in the class of all commutative (anti-commutative) algebras. For these clas
16 KB (2,433 words) - 21:48, 5 January 2016
[[Abelian group]] with the distributive action of a ring. A module is a generalization of a (linear)
[[ring]].
23 KB (3,918 words) - 04:31, 23 July 2018
{{Cite|Ch}} on conics and was systematized and used to great effect by H. Schubert in
{{Cite|Sc}}. The justification of Schubert's enumerative calculus and the verification of the numbers he obtained was the contents of Hilbert's 1
8 KB (1,263 words) - 08:49, 30 March 2012
...a square matrix $A = (a_{ij})$ of order $n$ over a commutative associative ring $R$ with unit 1'' is
where $i_1,\dots,i_n$ is a permutation of the numbers $1,\dots,n$ and $k$ is the number of inversions of the permutation $1\mapsto i_1,\dots,n\ma
11 KB (1,876 words) - 20:27, 30 November 2016
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and $ X $ (cf. [[Chern class|Chern class]]). It can be used to calculate the
10 KB (1,385 words) - 03:10, 2 March 2022
A polynomial $f$ with coefficients in a field or a commutative associative ring $K$ with a unit, which is a [[Symmetric function|symmetric function]] in it
and the power sums
5 KB (801 words) - 20:34, 13 September 2016
...ch thus becomes an Abelian group $\mathrm{Ext}^1_R(A,B)$, where $R$ is the ring over which $A$ is a module. This construction can be extended to $n$-fold e
...ential submodule]] of $X$). Every module has a maximal essential extension and this is the minimal [[injective module]] containing the given one.
2 KB (354 words) - 21:55, 30 October 2016
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be a Lie algebra over a commutative ring $ K $
21 KB (3,027 words) - 17:45, 4 June 2020
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and $ M $
12 KB (1,704 words) - 08:36, 26 March 2023
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and $ Y $,
5 KB (720 words) - 08:12, 6 June 2020
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defined over a complete discrete valuation ring $ R $
4 KB (651 words) - 08:25, 6 June 2020
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is an admissible monomorphism and $ B \in \mathop{\rm Ob} \mathfrak M $,
3 KB (532 words) - 08:28, 6 June 2020
.../old_files/data/P073/P.0703700 Polynomial and exponential growth in groups and algebras
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19 KB (2,908 words) - 20:20, 12 January 2024
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...concept of an arithmetical semi-group $G$ (cf. [[Abstract analytic number theory]]; [[Semi-group]]).
14 KB (2,037 words) - 09:45, 11 November 2023
...ra may be defined as a non-empty set $X$ with a [[binary relation]] $\ast$ and a constant $0$ satisfying the following axioms:
4) $x \ast y = 0$ and $y \ast x = 0$ imply $x = y$;
5 KB (892 words) - 02:43, 15 February 2024
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and $ N _ {2} $
8 KB (1,152 words) - 08:29, 6 June 2020
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...W. Feit and J.G. Thompson [[#References|[2]]], who showed that all finite groups of odd order are solvable.
15 KB (2,211 words) - 08:50, 26 March 2023
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be a structure series, and let $ \xi _ {n} $
3 KB (438 words) - 08:25, 6 June 2020