...f mathematics on the other, have determined the development of the concept of a number.
...provided by linguistics and ethnography. Primitive man clearly had no need of counting skills to determine whether or not a given collection was complete
23 KB (3,482 words) - 08:03, 6 June 2020
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...ups|Quantum groups]]) and a [[Super-group|super-group]], in which the role of Bose–Fermi statistics is now played by more general braid statistics. The
21 KB (3,130 words) - 17:42, 1 July 2020
...ic number fields $ K $ of finite degree over the field $ \mathbf Q $ of rational numbers (cf. [[Algebraic number|Algebraic number]]).
...ots \omega _{n} ) $ ; this means that each algebraic integer (i.e. element of $ O _{K} $ ) can be written in the form $ x _{1} \omega _{1} + \dots +
28 KB (4,440 words) - 22:00, 11 December 2019
''of a field $k$''
...ras, while the element inverse to the class of an algebra $A$ is the class of its [[opposite algebra]]. Each non-zero class contains, up to isomorphism,
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...ecture says that for a [[Finite group|finite group]] $G$ all torsion units of ${\bf Z} G$ are rationally conjugate to $\pm g$, $g \in G$:
9 KB (1,457 words) - 17:05, 26 January 2021
A partial differential equation (system) of the form
is a multi-index (a set of non-negative integers), $ | \alpha | = \sum {\alpha _ {i} } $,
18 KB (2,569 words) - 22:17, 5 June 2020
...159 : ~/encyclopedia/old_files/data/B110/B.1100850 Brauer characterization of characters
be a [[Finite group|finite group]]. A representation of $ G $
11 KB (1,659 words) - 08:43, 26 March 2023
of differentiations such that the set of restrictions of the elements of $ \Delta $
coincides with the set of differentiations on $ F _{0} $.
13 KB (1,981 words) - 20:02, 17 December 2019
This page is a copy of the article [[Extension of a differential field]] in order to test [[User:Maximilian_Janisch/latexlist
...entiations on $F _ { 0 }$. In turn, $F _ { 0 }$ is a differential subfield of $H ^ { \prime }$.
13 KB (1,976 words) - 13:36, 17 October 2019
$#C+1 = 230 : ~/encyclopedia/old_files/data/C023/C.0203110 Cohomology of algebras
...ule. This definition encompasses many cohomology theories of certain types of (universal) algebras.
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...$. They are indexed by the set $P ^ { + } \subset \mathfrak { h } ^ { * }$ of dominant integral weights $\lambda$ relative to $\Delta ^ { + }$.
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A process for obtaining a sequence of interpolation functions $ \{ f _ {n} ( z) \} $
of [[Interpolation|interpolation]] conditions. If the interpolation functions
12 KB (1,759 words) - 19:07, 11 January 2024
This page is a copy of the article [[Period mapping]] in order to test [[User:Maximilian_Janisch/l
...btained is considered as a point in the moduli variety of Hodge structures of a given type.
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of the base $ S $
of a family $ \{ X _{s} \} $
12 KB (1,699 words) - 09:49, 20 December 2019
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...ermat last theorem|Fermat last theorem]]). For details and generalizations of Iwasawa theory, see [[#References|[a10]]], [[#References|[a7]]], [[#Referen
19 KB (2,876 words) - 05:38, 15 February 2024
...ier integral|Fourier integral]]). Classical harmonic analysis — the theory
of Fourier series and Fourier integrals — underwent a rapid development, sti
.../h0464201.png" /> be a complex-valued square-summable function on a circle
of unit length (or on the segment <img align="absmiddle" border="0" src="https
66 KB (9,085 words) - 17:28, 31 March 2020
A very flexible geometric construction aimed to represent a family of similar objects (''fibres'' or ''fibers'', depending on the preferred spell
...of a smooth manifold. The [[covering]]s are also a special particular form of a topological bundle (with discrete fibers).
32 KB (5,299 words) - 12:27, 12 December 2020
...s is also called a height. From the point of view of estimating the number of rational points there are no essential differences between the functions in
Fundamental properties of the height. The function $h_L(P)$ is functorial with respect to $P$, i.e. f
34 KB (5,423 words) - 21:05, 10 February 2021
...Lie type'' if it can be obtained as a central [[Quotient group|quotient]] of a finite reductive group.
...n(q))$, where $Z(\SL_n(q))$ is the centre of $\SL_n(q)$, is a finite group of Lie type called the projective special linear group. This group is a [[Simp
48 KB (8,458 words) - 18:22, 13 August 2023
...tions (cf. [[Dirichlet L-function|Dirichlet $L$-function]]) form the basis of modern [[analytic number theory]]. In addition to Riemann's zeta-function o
which converges absolutely and uniformly in any bounded domain of the complex $s$-plane for which $\sigma\geq1+\delta$, $\delta>0$. If $\sigm
45 KB (7,251 words) - 02:20, 29 June 2022