Results 11 to 20 of about 109,686 (120)
Journal of Algebra, 2002 The authors generalize the notions of weak crossed products and Azumaya algebras under the class title ``weakly Azumaya algebras''. Among their results is a Wedderburn principal theorem (in the case where the center is a field). Their new monoid (which actually generalizes the Brauer group) is a union of groups they call ``stalks'', in each of which ...
Haile, Darrell, Rowen, Louis
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On Azumaya algebras with a finite automorphism group
International Journal of Mathematics and Mathematical Sciences, 2001 Let B be a ring with 1, C the center of B, and G a finite automorphism group of B. It is shown that if B is an Azumaya algebra such that B=⊕∑g∈GJg where Jg={b∈B|bx=g(x)b for all x∈B}, then there exist orthogonal central idempotents {fi∈C|i=1,2,…,m ...
George Szeto, Lianyong Xue
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Skew group rings which are Galois
International Journal of Mathematics and Mathematical Sciences, 2000 Let S*G be a skew group ring of a finite group G over a ring S. It is shown that if S*G is an G′-Galois extension of (S*G)G′, where G′ is the inner automorphism group of S*G induced by the elements in G, then S is a G-Galois extension of SG.
George Szeto, Lianyong Xue
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On a characterization of Azumaya algebras [PDF]
Publicacions Matemàtiques, 1988 A direct proof of Braun's characterization of Azumaya algebras is given.
W. Dicks, Dicks, Warren
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Pinching Azumaya algebras [PDF]
Journal of Pure and Applied Algebra, 2023 minor changes, to appear in J.
Johannes Fischer, Fischer, Johannes
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Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme [PDF]
, 2023 There is a new example for both obstructions.International audienceWe investigate quadratic pairs for Azumaya algebras with involutions over a base scheme S as defined by Calmès and Fasel, generalizing the case of quadratic pairs on central simple ...
Neher, Erhard +2 more
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Reduced K-theory of Azumaya algebras [PDF]
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
Hazrat, Roozbeh, Hazrat, R.
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The automorphisms of generalized cyclic Azumaya algebras [PDF]
, 2021 We define a nonassociative generalization of cyclic Azumaya algebras employing skew polynomial rings $D[t;\sigma]$, where $D$ is an Azumaya algebra of constant rank with center $C$ and $\sigma$ an automorphism of $D$, such that $\sigma|_{C}$ has finite ...
Pumpluen, S
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On the Grothendieck–Serre conjecture for classical groups
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 2884-2926, December 2022., 2022 Abstract We prove some new cases of the Grothendieck–Serre conjecture for classical groups. This is based on a new construction of the Gersten–Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue maps; the complex is shown to be exact when the ring is of dimension ⩽2$\leqslant 2$ (or ⩽
Eva Bayer‐Fluckiger +2 more
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The enumeration of finite rings
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3240-3262, December 2022., 2022 Abstract Let p$p$ be a fixed prime. We show that the number of isomorphism classes of finite rings of order pn$p^n$ is pα$p^\alpha$, where α=427n3+O(n5/2)$\alpha =\frac{4}{27}n^3+\mathnormal {O}(n^{5/2})$. This result was stated (with a weaker error term) by Kruse and Price in 1969; a problem with their proof was pointed out by Knopfmacher in 1973.
Simon R. Blackburn, K. Robin McLean
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