Results 11 to 20 of about 2,189 (114)

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
doaj   +2 more sources

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
doaj   +2 more sources

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, Uriya A. First, Raman Parimala   +2 more
wiley   +1 more source

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
wiley   +1 more source

On the structure of double complexes

Journal of the London Mathematical Society, Volume 104, Issue 2, Page 956-988, September 2021., 2021
Abstract We study consequences and applications of the folklore statement that every double complex over a field decomposes into so‐called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences easy to understand.
Jonas Stelzig
wiley   +1 more source

Some torsion classes in the Chow ring and cohomology of BPGLn

Journal of the London Mathematical Society, Volume 103, Issue 1, Page 127-160, January 2021., 2021
Abstract In the integral cohomology ring of the classifying space of the projective linear group PGLn (over C), we find a collection of p‐torsion classes yp,k of degree 2(pk+1+1) for any odd prime divisor p of n, and k⩾0. If, in addition, p2∤n, there are p‐torsion classes ρp,k of degree pk+1+1 in the Chow ring of the classifying stack of PGLn, such ...
Xing Gu
wiley   +1 more source

Weakly Azumaya Algebras

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
openaire   +1 more source

Topological Hochschild cohomology and generalized Morita equivalence [PDF]

, 2004
We explore two constructions in homotopy category with algebraic precursors in the theory of noncommutative rings and homological algebra, namely the Hochschild cohomology of ring spectra and Morita theory.
Andrew Baker, Andrey Lazarev, Generalized Morita Equivalence   +2 more
core   +3 more sources

Motives of Azumaya algebras [PDF]

Journal of the Institute of Mathematics of Jussieu, 2010
AbstractWe study the slice filtration for theK-theory of a sheaf of Azumaya algebrasA, and for the motive of a Severi-Brauer variety, the latter in the case of a central simple algebra of prime degree over a field. Using the Beilinson–Lichtenbaum conjecture, we apply our results to show the vanishing ofSK2(A) for a central simple algebraAof square-free
Kahn, Bruno, Levine, Marc
openaire   +2 more sources

Separable subalgebras of a class of Azumaya algebras

International Journal of Mathematics and Mathematical Sciences, 1998
Let S be a ring with 1, C the center of S, G a finite automorphism group of S of order n invertible in S, and SG the subnng of elements of S fixed under each element in G. It is shown that the skew group ring S*G is a G′-Galois extension of (S*G)G′ that
George Szeto
doaj   +1 more source