Results 41 to 50 of about 104 (97)
On the Witt group of the punctured spectrum of a regular semilocal ring
Journal of the London Mathematical Society, Volume 110, Issue 6, December 2024.Abstract Let R$R$ be a regular semilocal ring of dimension 4q+1⩾5$4q+1\geqslant 5$ which contains 12$\frac{1}{2}$, l⩾1$l\geqslant 1$ the number of maximal ideals of R$R$ which are assumed to be all of the same height, and U$U$ the punctured spectrum of R$R$, that is, SpecR$\operatorname{Spec}R$ without the maximal ideals. We show that the Witt ring W(U)
Stefan Gille, Ivan Panin
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Picard sheaves, local Brauer groups, and topological modular forms
Journal of Topology, Volume 17, Issue 2, June 2024.Abstract We develop tools to analyze and compare the Brauer groups of spectra such as periodic complex and real K$K$‐theory and topological modular forms, as well as the derived moduli stack of elliptic curves. In particular, we prove that the Brauer group of TMF$\mathrm{TMF}$ is isomorphic to the Brauer group of the derived moduli stack of elliptic ...
Benjamin Antieau +2 more
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The general Ikehata theorem for H‐separable crossed products
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 10, Page 657-662, 2000., 2000 Let B be a ring with 1, C the center of B, G an automorphism group of B of order n for some integer n, CG the set of elements in C fixed under G, Δ = Δ(B, G, f) a crossed product over B where f is a factor set from G × G to U(CG). It is shown that Δ is an H‐separable extension of B and VΔ(B) is a commutative subring of Δ if and only if C is a Galois ...
George Szeto, Lianyong Xue
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$K$-Theory of Azumaya algebras
Irish Mathematical Society Bulletin, 2010 For an Azumaya algebra $A$ which is free over its centre $R$, we prove that the $K$-theory of $A$ is isomorphic to $K$-theory of $R$ up to its rank torsion. We observe that a graded central simple algebra, graded by an abelian group, is a graded Azumaya algebra and it is free over its centre.
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Azumaya algebras with involutions
Journal of Algebra, 1990 Let R be a commutative ring and S/R an étale quadratic extension. Br(-) is the Brauer group and \({}_ 2Br(\)-) its 2-torsion. This paper studies the problem of when the sequence \[ _ 2Br(R)\quad \to^{Res}\quad_ 2Br(S)\quad \to^{Cores}\quad_ 2Br(R) \] is exact. If R, S are fields and char \(R\neq 2\), the sequence is known to be exact. From the authors'
Knus, M.-A, Parimala, R, Srinivas, V
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Categorical Torelli theorems: results and open problems. [PDF]
Rend Circ Mat Palermo, 2023 Pertusi L, Stellari P.
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A characterization of Azumaya algebras
Journal of Pure and Applied Algebra, 1976 AbstractLet R be a commutative ring with identity 1, and A a finitely generated R-algebra. It is shown that A is an Azumaya R-algebra if and only if every stalk of the Pierce sheaf induced by A is an Azumaya algebra.
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Deformations of Azumaya algebras
, 2006 In this paper we compute the deformation theory of a special class of algebras, namely of Azumaya algebras on a manifold ($C^{\infty}$ or complex analytic).
Nest, Ryszard +3 more
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Azumaya algebras with involution
Journal of Algebra, 1978 One of the highpoints of the theory of central simple algebras as developed in the 1920s and 1930s was the results of Albert concerning simple rings with involution. A part of his results was the characterization of those finite dimensional central simple algebras which admit an involution.
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Azumaya’s Canonical Module and Completions of Algebras [PDF]
Nagoya Mathematical Journal, 1973 We are concerned with an algebra S over a commutative ring. Precisely S is a non-commutative ring with identity which is also a finitely generated unital R module such that r(xy) = (rx)y = x(ry) for r in R and x, y ∈ S. In section one, we assume A is a commutative, Artinian ring. Following Goro Azumaya (see (1, p.
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