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...

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...

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...

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...

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...

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...

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...

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...

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...

within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain...

In mathematics, in linear algebra and functional analysis, a cyclic subspace is a certain special subspace of a vector space associated with a vector...

This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations...

from central simple algebras over R / m {\displaystyle R/{\mathfrak {m}}} . There is a class of Azumaya algebras called cyclic algebras which generate all...

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...

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...

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...

related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham...

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...

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...

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...

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...

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called...

several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding...

permutation in terms of its constituent cycles In commutative algebra and linear algebra, cyclic decomposition refers to writing a finitely generated module...

Appendix:Glossary of abstract algebra in Wiktionary, the free dictionary. Abstract algebra is the subject area of mathematics that studies algebraic structures, such...

In algebra, a unit or invertible element of a ring is an invertible element for the multiplication of the ring. That is, an element u of a ring R is a...

In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or...

SU(2) × SU(2) = S3 × S3. In terms of algebraic topology, for n > 2 the fundamental group of SO(n, R) is cyclic of order 2, and the spin group Spin(n)...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation...