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The valuation ring $ R= \{ {a \in K } : {| a | \leq 1 } \} $
8 KB (1,161 words) - 08:25, 6 June 2020
...ntral simple algebras. This group is also known as the Brauer group of $k$ and is denoted by $\Br(k)$. The zero element of this group is the class of full
.... The general form of the reciprocity law is formulated in terms of Brauer groups.
7 KB (1,232 words) - 12:12, 30 December 2015
$#C+1 = 130 : ~/encyclopedia/old_files/data/I052/I.0502040 Intersection theory
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12 KB (1,730 words) - 22:13, 5 June 2020
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and $ q $
8 KB (1,160 words) - 08:05, 6 June 2020
...ess a synonym for "Hopf algebra" . More precisely, the category of quantum groups is defined in [[#References|[a1]]] to be dual to the category of Hopf algeb
...pace" is understood to be "affine scheme" or "compact topological space" , and "algebra" is understood to mean "C*-algebra" ). So one can translate the de
18 KB (2,674 words) - 19:09, 16 December 2019
$#C+1 = 79 : ~/encyclopedia/old_files/data/M065/M.0605040 Motives, theory of
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8 KB (1,246 words) - 18:08, 10 July 2024
...ring of polynomials in a finite number of variables over a field or over a ring of integers any ideal is generated by a finite number of elements (has a fi
and only for them. This theorem, which was obtained by D. Hilbert in 1892, was
18 KB (2,720 words) - 19:17, 19 December 2019
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and every pair of topological spaces $ ( X, Y) $,
8 KB (1,093 words) - 08:21, 13 January 2024
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A fundamental theorem in [[K-theory| $ K $-
3 KB (474 words) - 13:07, 24 December 2020
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and, in accordance with Poincaré duality, a cohomology class $ \gamma (Z) \i
12 KB (1,877 words) - 17:38, 16 July 2024
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such that the cohomology groups $ H ^ {p} ( X , A ; G ) $
9 KB (1,321 words) - 17:45, 4 June 2020
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...ategory]] has this property). In such categories an object is injective if and only if it is a direct summand of any object containing it. For the objects
4 KB (643 words) - 22:12, 5 June 2020
''of a Lie algebra $ \mathfrak{g} $ over a commutative ring $ \mathbb{k} $ with a unit element''
...f Lie algebras, i.e., $ \sigma $ is a $ \mathbb{k} $-linear transformation and $ \sigma([x,y]) = \sigma(x) \sigma(y) - \sigma(y) \sigma(x) $ for all $ x,y
6 KB (970 words) - 18:59, 5 April 2023
$#C+1 = 149 : ~/encyclopedia/old_files/data/K055/K.0505580 Knot and link groups
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12 KB (1,807 words) - 18:41, 13 January 2024
$#C+1 = 35 : ~/encyclopedia/old_files/data/K110/K.1100080 Kerdock and Preparata codes
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6 KB (942 words) - 02:58, 18 May 2022
$#C+1 = 157 : ~/encyclopedia/old_files/data/R077/R.0707130 Radical of rings and algebras
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16 KB (2,540 words) - 08:09, 6 June 2020
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and is defined for all natural indices $ i $.
13 KB (1,910 words) - 19:40, 7 January 2024
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The branch of algebra studying the properties of commutative rings and objects relating to them (ideals, modules, valuations, etc., cf. [[Ideal|Id
16 KB (2,400 words) - 17:45, 4 June 2020
...generalization of the concept of a divisor of an element of a commutative ring. First introduced by E.E. Kummer
...$. The image $\phi(a)\in D_0$ of an element $a\in A^*$ is denoted by $(a)$ and is called the principal divisor of the element $a$. One says that $a\in A^*
16 KB (2,808 words) - 16:01, 27 July 2024
...induced fibration in topology,
and extension of the
ring of scalars in the
theory of modules.
...//www.encyclopediaofmath.org/legacyimages/b/b015/b015310/b01531014.png" />
and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
11 KB (1,514 words) - 17:53, 18 July 2024