[[Cohomology ring|cohomology ring]] of a complex flag manifold $G/P$ (cf. also
[[Linear algebraic group|linear algebraic group]] and $P$ is a
3 KB (371 words) - 18:45, 30 March 2012
...commensurable with the group $G_O$ of $O$-points of $G$, where $O$ is the ring of integers of $k$. An arithmetic group $H \cap G_{\mathbb{R}}$ is a [[Disc
...m $k$ to $\mathbb{Q}$, is called an arithmetic group. In the theory of Lie groups the name arithmetic subgroups is also given to images of arithmetic subgrou
4 KB (527 words) - 20:14, 14 October 2014
$#C+1 = 33 : ~/encyclopedia/old_files/data/G044/G.0404620 Gorenstein ring
Please remove this comment and the {{TEX|auto}} line below,
4 KB (623 words) - 19:42, 5 June 2020
...1 = 73 : ~/encyclopedia/old_files/data/D033/D.0303180 Discretely\AAhnormed ring,
Please remove this comment and the {{TEX|auto}} line below,
5 KB (800 words) - 19:36, 5 June 2020
...all png images have been replaced by TeX code, please remove this message and the {{TEX|semi-auto}} category.
...$R$-) module (cf. also [[Associative rings and algebras|Associative rings and algebras]]; [[Module|Module]]). Then $N$ is a Whitehead test module for pro
5 KB (732 words) - 17:46, 1 July 2020
$#C+1 = 28 : ~/encyclopedia/old_files/data/S083/S.0803470 Schur ring
Please remove this comment and the {{TEX|auto}} line below,
3 KB (500 words) - 18:57, 11 January 2024
Please remove this comment and the {{TEX|auto}} line below,
and $ q $
2 KB (346 words) - 18:45, 11 April 2023
The ''Chow ring'' of a non-singular quasi-projective algebraic variety
...n terms of intersections of cycles (cf. [[Intersection theory|Intersection theory]]).
4 KB (714 words) - 21:54, 24 April 2012
Please remove this comment and the {{TEX|auto}} line below,
over a ring $ R $
3 KB (439 words) - 08:09, 6 June 2020
Please remove this comment and the {{TEX|auto}} line below,
of a ring $ A $
6 KB (990 words) - 10:59, 29 May 2020
Please remove this comment and the {{TEX|auto}} line below,
...can study the structure of the algebraic system, its representation theory and harmonic analysis on the system. A [[Representation of a topological group|
3 KB (399 words) - 22:12, 5 June 2020
...pecially useful for generalizations of the Galois theory of finite, normal and separable field extensions.
...F$ is generated by $P$ and $G$; indeed, it is the [[cross product]] of $P$ and $G$.
3 KB (470 words) - 19:10, 9 November 2016
Please remove this comment and the {{TEX|auto}} line below,
By the Pontryagin–Thom theorem, there is a ring spectrum $ MU $(
4 KB (633 words) - 08:47, 26 March 2023
Assertions on the invariance of the groups $ K _{i} (R) $
or their subgroups, given certain special extensions of the ground ring $ R $(
7 KB (972 words) - 19:10, 5 April 2023
''of degree (order) $\def\SL{\textrm{SL}}\def\GL{\textrm{GL}} n$ over a ring $R$''
...tance here: the ordinary determinant in the case when $R$ is a commutative ring, the non-commutative Dieudonné determinant (cf.
6 KB (988 words) - 22:16, 10 January 2015
...valid. There exists a group $K(C)$, called the Grothendieck group of $C$, and an additive mapping $k:\mathrm{Ob}(C)\to K(C)$, known as the universal mapp
...nerators — to each object $L \in C$, there corresponds a generator $[L]$ — and by the relations $[L]-[N]-[M]=0$ for each exact sequence $0 \to L \to M \to
4 KB (701 words) - 06:11, 26 March 2023
...t is hard to say whether field theory, the theory of finite groups and the theory of finite-dimensional Lie algebras should be regarded as general algebra.
...t developed theories are those of partially ordered and topological groups and rings.
5 KB (725 words) - 21:52, 30 March 2012
A pre-$\lambda$-ring is a commutative ring $R$ with identity element $1$ and a set of mappings $\lambda^n : R \rightarrow R$, $n = 0,1,2,\ldots$ such th
...ng exterior powers. For instance, for $M = \text{pt}$, $K(M) = \mathbf{Z}$ and the $\lambda$-structure is given by $\lambda^n(m) = \binom{m}{n}$ (binomial
10 KB (1,721 words) - 07:44, 23 March 2016
Please remove this comment and the {{TEX|auto}} line below,
...n which is an anti-isomorphism. In particular, it is defined for any group ring $ \mathbf Z [ \pi _ {1} ( X)] $,
7 KB (997 words) - 08:28, 6 June 2020
...y of polycyclic groups. If $k$ is an algebraic extension of a finite field and $G$ is a finite extension of a polycyclic group, then any simple $kG$-modul
...[2]</TD> <TD valign="top"> B.A.F. Wehrfritz, "Three lectures on polycyclic groups" , Queen Mary College London (1973)</TD></TR></table>
4 KB (588 words) - 19:59, 11 April 2014