Results 11 to 20 of about 231,292 (124)

Pinching Azumaya algebras [PDF]

Journal of Pure and Applied Algebra, 2023
minor changes, to appear in J.
Johannes Fischer, Fischer, Johannes
openaire   +3 more sources

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

The closed socle of an Azumaya algebra [PDF]

Proceedings of the American Mathematical Society, 1980
If R is a Noetherian ring and A is an Azumaya algebra over R then an ideal H
F. R. DeMeyer
openaire   +2 more sources

A characterization of Azumaya algebras [PDF]

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.
Szeto, George
openaire   +3 more sources

Counterexamples in involutions of Azumaya algebras [PDF]

Journal of Algebra
21 ...
Uriya First, Ben Williams
core   +4 more sources

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.
openaire   +4 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