In algebra, a cyclic division algebra is one of the basic examples of a division algebra over a field and plays a key role in the theory of central simple...
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In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused...
36 KB (4,113 words) - 03:36, 18 July 2024
Factor system (redirect from Crossed product algebra)
product of G with A. If a group algebra is given, then a factor system f modifies that algebra to a skew-group algebra by modifying the group operation...
7 KB (982 words) - 11:35, 3 October 2023
Brauer group (category Algebraic number theory)
ζ. For nonzero elements a and b of K, the associated cyclic algebra is the central simple algebra of degree n over K defined by ( a , b ) ζ = K ⟨ u , v...
22 KB (2,941 words) - 20:50, 16 July 2024
In abstract algebra, every subgroup of a cyclic group is cyclic. Moreover, for a finite cyclic group of order n, every subgroup's order is a divisor of...
6 KB (754 words) - 08:35, 6 February 2023
Ring (mathematics) (redirect from Ring (algebra))
the Cartan–Brauer–Hua theorem. A cyclic algebra, introduced by L. E. Dickson, is a generalization of a quaternion algebra. A semisimple module is a direct...
99 KB (13,673 words) - 08:52, 19 October 2024
theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation...
13 KB (2,039 words) - 05:13, 6 June 2024
Gelfand–Naimark–Segal construction (category C*-algebras)
within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain...
14 KB (2,010 words) - 21:11, 1 October 2024
quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a matrix algebra by extending...
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In mathematics, the notion of a cyclic and separating vector is important in the theory of von Neumann algebras, and in particular in Tomita–Takesaki...
4 KB (498 words) - 13:51, 4 November 2021
from central simple algebras over R / m {\displaystyle R/{\mathfrak {m}}} . There is a class of Azumaya algebras called cyclic algebras which generate all...
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This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations...
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In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order is not modeled...
53 KB (6,381 words) - 04:47, 23 July 2024
Abelian extension (redirect from Cyclic extension)
In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is...
2 KB (340 words) - 11:36, 16 May 2023
related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham...
11 KB (1,544 words) - 14:31, 29 May 2024
In mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept...
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Cycle graph (algebra), a diagram representing the cycles determined by taking powers of group elements Circulant graph, a graph with cyclic symmetry Cycle...
2 KB (261 words) - 02:33, 8 May 2023
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called...
31 KB (4,082 words) - 07:56, 15 October 2024
E8 (mathematics) (redirect from E8 Lie algebra)
several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding...
46 KB (6,107 words) - 15:48, 1 October 2024
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting...
26 KB (5,114 words) - 17:30, 4 January 2024
domain, forming an important chapter of linear algebra. Any group of prime order is isomorphic to a cyclic group and therefore abelian. Any group whose...
36 KB (5,284 words) - 17:38, 8 October 2024
Cycle decomposition (redirect from Cyclic decomposition)
permutation in terms of its constituent cycles In commutative algebra and linear algebra, cyclic decomposition refers to writing a finitely generated module...
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In mathematics, in linear algebra and functional analysis, a cyclic subspace is a certain special subspace of a vector space associated with a vector...
5 KB (954 words) - 06:52, 17 December 2023
Finite group (section Cyclic groups)
In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or...
15 KB (1,831 words) - 21:48, 27 January 2024
E7 (mathematics) (redirect from E7 Lie algebra)
of the (adjoint) complex form, compact real form, or any algebraic version of E7 is the cyclic group Z/2Z, and its outer automorphism group is the trivial...
19 KB (2,766 words) - 21:58, 12 June 2024
Group (mathematics) (redirect from Group (algebra))
group of a field is necessarily cyclic. See Lang 2002, Theorem IV.1.9. The notions of torsion of a module and simple algebras are other instances of this...
101 KB (13,147 words) - 02:07, 28 September 2024
E6 (mathematics) (category Algebraic groups)
is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras e 6 {\displaystyle {\mathfrak {e}}_{6}} , all of which have...
28 KB (3,820 words) - 21:54, 12 June 2024
Appendix:Glossary of abstract algebra in Wiktionary, the free dictionary. Abstract algebra is the subject area of mathematics that studies algebraic structures, such...
12 KB (1,129 words) - 10:50, 10 October 2024
Special unitary group (redirect from Special unitary Lie algebra)
connected. Algebraically, it is a simple Lie group (meaning its Lie algebra is simple; see below). The center of SU(n) is isomorphic to the cyclic group Z...
34 KB (5,711 words) - 08:07, 3 October 2024
In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation...
18 KB (2,553 words) - 15:03, 27 August 2024