...all png images have been replaced by TeX code, please remove this message and the {{TEX|semi-auto}} category.
...)$ is a derivation of $V$ (cf. also [[Derivation in a ring|Derivation in a ring]]). Thus one denotes $\{ L ( x , y ) \} _ { \text{span} }$ by $\operatornam
3 KB (559 words) - 16:43, 15 March 2023
and any non-zero vector $ v \in V $
...the theorem on finite generation of the algebra of invariants of reductive groups of automorphisms of an algebra of finite type over a field (see [[Hilbert t
6 KB (818 words) - 12:00, 16 December 2019
An invariant of cohomology type associated with schemes in [[Algebraic K-theory|algebraic $ K $-
theory]]. More precisely, in algebraic $ K $-
8 KB (1,120 words) - 20:06, 31 October 2023
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...fference set|Difference set]] (Vol. 3). For an extensive discussion of the theory of Abelian difference sets, see also [[#References|[a1]]], Chap. VI.
9 KB (1,331 words) - 19:36, 13 February 2024
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...tre $Z _ { G }$ of $G$ (cf. also [[Centre of a group|Centre of a group]]), and coincides with $Z _ { G }$ if $G$ is connected. The image $\text{Ad}( G )$
8 KB (1,184 words) - 16:59, 1 July 2020
groups ${\rm Gr}$. The category $S-{\rm Gr}$ of group schemes over $S$ is defined
multiplicative) group of the ring of sections of the structure sheaf
5 KB (831 words) - 21:59, 5 March 2012
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and negatively graded if $ A _ {n} = 0 $
2 KB (330 words) - 16:25, 23 November 2023
...|rational representation]] of $k$ in a finite-dimensional vector space $V$ and any non-zero vector $v \in V$ fixed by $k$, there is a $k$-invariant homoge
...the theorem on finite generation of the algebra of invariants of reductive groups of automorphisms of an algebra of finite type over a field (see [[Hilbert t
6 KB (862 words) - 13:44, 17 October 2019
...her with a unary [[relation symbol]] for being an element of the valuation ring, or a binary relation symbol for valuation divisibility $v(x)\leq v(y)$ (cf
...t in the proof that Hilbert's 10th problem has a positive solution for the ring of all algebraic integers (see [[Algebraic Diophantine equations|Algebraic
12 KB (1,846 words) - 09:28, 26 November 2016
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The groups
19 KB (2,870 words) - 09:48, 26 March 2023
...r $K$. 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.
15 KB (2,312 words) - 13:44, 17 October 2019
...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