Results 41 to 50 of about 633,805 (104)
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).
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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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DIFFERENTIAL OPERATORS ON AZUMAYA ALGEBRAS AND HEISENBERG ALGEBRAS
Communications in Algebra, 2001 We use the definition of differential operators on noncommutative rings given by V.Lunts and A.Rosenberg to find the differential operators on Azumaya algebras and the Heisenberg algebras.
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On the Azumaya locus of almost commutative algebras [PDF]
Proceedings of the American Mathematical Society, 2010 We prove a general statement which implies the coincidence of the Azumaya and smooth loci of the center of an algebra in positive characteristic, provided that the spectrum of its associated graded algebra has a large symplectic leaf. In particular, we show that for a symplectic reflection algebra, the smooth and the Azumaya loci coincide.
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On a characterization of Azumaya algebras
Publicacions Matemàtiques, 1988 A direct proof of Braun's characterization of Azumaya algebras is given.
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Reduced K-theory of Azumaya algebras
Journal of Algebra, 2006 Consider an Azumaya algebra \(A\) over a commutative ring \(R\), and let \(K_i\) denote the Quillen \(K\)-functor. For \(i\geq 0\), one defines \(ZK_i(A)\) and \(CK_i(A)\) as the kernel and co-kernel of the map \(K_i(R)\to K_i(A)\), induced by the embedding \(R\to A\). The author defines a \(D\)-functor from a category of algebras to Abelian groups, as
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