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In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with...

of a maximal subfield of D over the center. Given a field F, the Brauer equivalence classes of simple (contains only trivial two-sided ideals) associative...

and B are called similar (or Brauer equivalent) if their division rings S and T are isomorphic. The set of all equivalence classes of central simple algebras...

Morita equivalence. Such algebras coming from Brauer trees are called Brauer tree algebras. Feit (1984) described the possibilities for Brauer trees....

The Brauer character of a representation determines its composition factors but not, in general, its equivalence type. The irreducible Brauer characters...

that yields an equivalence is automatically additive. The Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central...

Witt decomposition. The Witt group of k is the abelian group W(k) of equivalence classes of non-degenerate symmetric bilinear forms, with the group operation...

result on Clifford modules is that the Morita equivalence class of a Clifford algebra (the equivalence class of the category of Clifford modules over...

conjectured that every nonabelian finite simple group has even order. Richard Brauer (1957) suggested using the centralizers of involutions of simple groups...

operation. This forms a group structure on the set of such equivalence classes called the Brauer group, denoted Br ( R ) {\displaystyle {\text{Br}}(R)} ...

Bilinear operator Binary operation Commutative Congruence relation Equivalence class Equivalence relation Lattice (group) Lattice (discrete subgroup) Multiplication...

allows for a definition of bisimulation equivalence. In the π-calculus, the definition of bisimulation equivalence (also known as bisimilarity) may be based...

form by Carl Friedrich Gauss, a composition law was defined on certain equivalence classes of forms. This gave a finite abelian group, as was recognised...

this set of vector lines. This set can be the set of equivalence classes under the equivalence relation between vectors defined by "one vector is the...

monomorphism Ring isomorphism Skolem–Noether theorem Graded algebra Morita equivalence Brauer group Constructions Direct sum of rings, Product of rings Quotient...

theorems determining when two rings have "equivalent" module categories Cartan–Brauer–Hua theorem gives insight on the structure of division rings Wedderburn's...

manifold) Brauer–Nesbitt theorem (representation theory of finite groups) Brauer–Siegel theorem (number theory) Brauer–Suzuki theorem (finite groups) Brauer–Suzuki–Wall...

formal quotients x ∖ y {\displaystyle x\backslash y} subject to the equivalence relation x ∖ y = u ∖ v iff v = u / x ⋅ y {\displaystyle x\backslash y=u\backslash...

the real numbers and the quaternions, where the Brauer group is the set of all CSAs, up to equivalence relation of one CSA being a matrix ring over another...

Generalized Riemann hypothesis Deuring–Heilbronn phenomenon Class number problem Brauer–Siegel theorem Siegel–Walfisz theorem See Iwaniec (2006). See Satz 4, §5...