areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative K-algebra A that is simple, and for which the center...

k-algebra is central if its center is k and is simple if it is a simple ring. Since the center of a simple k-algebra is a field, any simple k-algebra is...

In abstract algebra, a branch of mathematics, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular...

contains a simple algebra. Simple group Simple ring Central simple algebra Lampe, W.A.; Taylor, W. (1982). "Simple algebras in varieties". Algebra Universalis...

classification of finite simple groups says that most finite simple groups arise as the group G(k) of k-rational points of a simple algebraic group G over a finite...

are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist...

A central simple algebra over K is a matrix algebra over a (finite-dimensional) division algebra with center K. For example, the central simple algebras...

version for central simple algebras, as it appears in (Knapp 2007, p.115): Theorem: If A is a finite-dimensional central simple algebra over a field...

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...

Birman–Wenzl algebra Boolean algebra Borcherds algebra Brauer algebra C*-algebra Central simple algebra Clifford algebra Cluster algebra Dendriform algebra Differential...

of unity. An Okubo algebra is an algebra constructed in this way from the trace-zero elements of a degree-3 central simple algebra over a field. Unital...

In mathematics, an Azumaya algebra is a generalization of central simple algebras to R {\displaystyle R} -algebras where R {\displaystyle R} need not...

SK_{1}(A)} is trivial for any central simple algebra over a number field, but Platonov has given examples of algebras of degree prime squared for which...

characterizes the automorphisms of simple rings. It is a fundamental result in the theory of central simple algebras. The theorem was first published by...

module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field extension L of the field...

theory Degree of unsolvability in recursion theory Degree of a central simple algebra Degree of a permutation group, the number of elements that are permuted...

In algebraic number theory, the Albert–Brauer–Hasse–Noether theorem states that a central simple algebra over an algebraic number field K which splits...

The list of simple Lie groups can be used to read off the list of simple Lie algebras and Riemannian symmetric spaces. Together with the commutative Lie...

Harish-Chandra isomorphism. The center of a simple algebra is a field. Center of a group Central simple algebra Morita equivalence "vector spaces – A linear...

finite-dimensional central simple algebras over a field k {\displaystyle k} to the problem of classifying finite-dimensional central division algebras over k {\displaystyle...

ring is −∞. The zero ring is semisimple but not simple. The zero ring is not a central simple algebra over any field. The total quotient ring of the zero...

(identity matrix) as the unity. Central simple algebra Clifford algebra Hurwitz's theorem (normed division algebras) Generic matrix ring Sylvester's...

radical). If the algebra is finite-dimensional this is equivalent to saying that it can be expressed as a Cartesian product of simple subalgebras. The...

algebra is an associative algebra over the centre. 3.  A central simple algebra is a central algebra that is also a simple ring. centralizer 1.  The centralizer...

(mathematics), Division ring, division algebra Simple ring, Central simple algebra, Semisimple ring, Semisimple algebra Primitive ring, Semiprimitive ring...

an algebraic variety V which becomes isomorphic to a projective space over an algebraic closure of K. The varieties are associated to central simple algebras...

closer non-commutative analog are central simple algebras (CSAs) – ring extensions over a field, which are simple algebra (no non-trivial 2-sided ideals...

equivalence classes of central simple algebras of finite rank over K and addition is induced by the tensor product of algebras. It arose out of attempts...

crossed product algebra A is a central simple algebra (CSA) of degree equal to [L : K]. The converse holds: every central simple algebra over K that splits...

and classification of Lie groups in terms of Lie algebras, which are simpler objects of linear algebra. In more detail: for any Lie group, the multiplication...