$#C+1 = 92 : ~/encyclopedia/old_files/data/R082/R.0802480 Rings and algebras
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21 KB (3,225 words) - 09:25, 13 July 2022
...The discriminant is symmetric with respect to the roots of the polynomial and may therefore be expressed in terms of the coefficients of this polynomial.
...ula|Cardano formula]]) is $-27 q^2-4p^3$. If $f(x)$ is a polynomial over a field of characteristic zero, then
16 KB (2,947 words) - 08:53, 9 December 2016
Baxter algebras originated in the following problem in fluctuation theory: Find the distribution functions of the maxima $\max\{0, S_1, \ldots, S_n \
...n(t)$ is the [[characteristic function]] of $\max\{0, S_1, \ldots, S_n \}$ and $\psi_k(t)$ is the characteristic function of $\max\{0, S_k \}$. Spitzer's
6 KB (960 words) - 07:40, 18 November 2023
....encyclopediaofmath.org/legacyimages/m/m063/m063460/m06346010.png" /> is a
field with respect to the usual [[pointwise operation]]s followed by redefinition
...fmath.org/legacyimages/m/m063/m063460/m06346022.png" /> coincides with the
field of fractions of the ring <img align="absmiddle" border="0" src="https://www
44 KB (5,974 words) - 22:47, 29 November 2014
[[Field|field]] $L$ of characteristic $p>0$ is an exotic $A$-module structure on the addi
...omorphism rings, the existence of analytic "Weierstrass uniformizations" , and the moduli theories (modular varieties, modular forms; cf. also
19 KB (3,204 words) - 20:11, 14 April 2012
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and is called the stabilizer or stationary subgroup of the point $ x $
13 KB (2,049 words) - 19:35, 17 January 2024
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over a field $ K $
20 KB (2,828 words) - 19:11, 26 March 2023
and for $k_i \ge 1$,
and a corresponding multinomial theorem. The Wick exponential is defined as
13 KB (1,983 words) - 18:50, 11 December 2020
...r series in the associative but non-commutative variables $ u $ and $ v $, and $ \widehat{L} $ is the closure of $ L $ in $ \widehat{A} $. Then the mappin
...ormula provides an expression for $ u \circ v $ as a power series in $ u $ and $ v $:
6 KB (1,020 words) - 17:41, 4 May 2017
as the sum of a semi-simple and a nilpotent endomorphism that commute with each other: $ g = g _{s} + g _
and $ g _{n} $
10 KB (1,474 words) - 02:51, 25 February 2022
over a field $ k $
the adjoint transformation) and $ \Lambda _{p} ( x ,\ y ) $
10 KB (1,443 words) - 10:14, 17 December 2019
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...\rangle$ denote an [[Inner product|inner product]] on $\mathbf{C} ^ { n }$ and let $\| .\|$ be the induced [[Norm|norm]].
9 KB (1,275 words) - 17:43, 1 July 2020
...erous applications in algebraic geometry, class field theory and cobordism theory.
A formal group over a field $ k $
17 KB (2,537 words) - 22:38, 15 December 2019
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and $ \Delta _ {2} $);
17 KB (2,406 words) - 20:00, 12 January 2024
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...be determined by means of computations involving finitely many steps, i.e. field operations in $k$. Any $R$-module for $R : = k [ X _ { 1 } , \dots , X _ {
10 KB (1,498 words) - 14:47, 3 February 2024
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...ty of $C$, see [[#References|[a1]]]. For an interplay between the geometry and the algebra, see [[#References|[a2]]].
16 KB (2,510 words) - 17:43, 1 July 2020
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and for each point $ x _ {t} $
10 KB (1,455 words) - 06:59, 6 March 2024
...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
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and each element $ h \in X $
6 KB (901 words) - 16:08, 1 April 2020
...erences|[a1]]] have their origins in physics in earlier work of N. Seiberg and E. Witten [[#References|[a2]]], [[#References|[a3]]].
...ection|connection]] $A$ on a line bundle $L$ over $M$ and a "local spinor field" $\psi$. The Seiberg–Witten equations are then
16 KB (2,663 words) - 10:57, 13 February 2024