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Azumaya algebra

In mathematics, an Azumaya algebra is a generalization of central simple algebras to R {\displaystyle R} -algebras where R {\displaystyle R} need not be a field. Such a notion was introduced in a 1951 paper of Goro Azumaya, for the case where R {\displaystyle R} is a commutative local ring. The notion was developed further in ring theory, and in…

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Over a ring

Brauer group of a ring

Skolem–Noether theorem

On a scheme

Applications

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Azumaya algebra

Nodes56
Edges55
Triples61
Avg. degree1.96
Density0.035714
Components1

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Azumaya algebra

Top relations

related to Cyclic algebras · 8
Azumaya algebra → Azumaya, Br, Brauer, Gal, Galois, Given, L/K, There
related to Skolem–Noether theorem · 8
Azumaya algebra → Azumaya, In, Meaning, Noether, One, PGL, Skolem, This
related to Example in positive characteristic · 7
Azumaya algebra → Azumaya, Frobenius, Geometric Langlands, Let, Nonabelian Hodge, Then, This Azumaya
related to On a scheme · 7
Azumaya algebra → An Azumaya, Azumaya, Cohomology, Grothendieck, Milne, This, Two Azumaya
has application · 6
Azumaya algebra → Azumaya, Brauer, Hasse, The Manin, There, Yuri Manin
related to Examples over a field · 6
Azumaya algebra → Artin, Azumaya, For, Over, These, Wedderburn
related to Brauer group of a ring · 5
Azumaya algebra → Azumaya, Brauer, In, Over, Then
related to Over a ring · 5
Azumaya algebra → An Azumaya, End, Morita, The, There
related to Example over Pn · 4
Azumaya algebra → Azumaya, End, For, Over
related to Example over Spec(Z[1/n]) · 4
Azumaya algebra → Azumaya, Hilbert, Spec, The

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displaystyle azumaya group algebra algebras field text brauer ring cohomology local mathbb galois classes theorem otimes given sheaf mathcal cyclic

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SubjectPredicateObjectConfidenceSrc
Azumaya algebrais ageneralization of central simple algebras to R0.90text
Azumaya algebrahas applicationThere0.60section
Azumaya algebrahas applicationAzumaya0.60section
Azumaya algebrahas applicationYuri Manin0.60section
Azumaya algebrahas applicationThe Manin0.60section
Azumaya algebrahas applicationHasse0.60section
Azumaya algebrahas applicationBrauer0.60section
Azumaya algebrarelated to Brauer group of a ringOver0.60section
Azumaya algebrarelated to Brauer group of a ringAzumaya0.60section
Azumaya algebrarelated to Brauer group of a ringIn0.60section
Azumaya algebrarelated to Brauer group of a ringBrauer0.60section
Azumaya algebrarelated to Brauer group of a ringThen0.60section

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