Results 41 to 50 of about 109,686 (120)
On Hopf Galois Hirata extensions
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 64, Page 4033-4039, 2003., 2003 Let H be a finite‐dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*‐Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB(BH)#H. A sufficient condition is also given for B to be an H*‐Galois Azumaya extension of BH.
George Szeto, Lianyong Xue
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On ring homomorphisms of Azumaya algebras [PDF]
, 2005 The main theorem (Theorem 4.1) of this paper claims that any ring morphism from an Azumaya algebra of constant rank over a commutative ring to another one of the same constant rank and over a reduced commutative ring induces a ring morphism between the ...
Adjamagbo, Kossivi +2 more
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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
openaire +1 more source
The Galois algebras and the Azumay Galois extensions
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 1, Page 37-42, 2002., 2002 Let B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K = {g ∈ G | g(c) = c for all c ∈ C}, Jg{b ∈ B | bx = g(x)b for all x ∈ B} for each g ∈ K, and BK = (⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by K.
George Szeto, Lianyong Xue
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On certain classes of Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 5, Page 315-321, 2001., 2001 Relations between the following classes of Galois extensions are given: (1) centrally projective Galois extensions (CP‐Galois extensions), (2) faithfully Galois extensions, and (3) H‐separable Galois extensions. Moreover, it is shown that the intersection of the class of CP‐Galois extensions and the class of faithfully Galois extensions is the class ...
George Szeto, Lianyong Xue
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Pfister's local-global principle for Azumaya algebras with involution [PDF]
, 2023 We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is $2$-primary torsion.
Astier, Vincent, Unger, Thomas
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Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract Given an associative C$\mathbb {C}$‐algebra A$A$, we call A$A$ strongly rigid if for any pair of finite subgroups of its automorphism groups G,H$G, H$, such that AG≅AH$A^G\cong A^H$, then G$G$ and H$H$ must be isomorphic. In this paper, we show that a large class of filtered quantizations are strongly rigid.
Akaki Tikaradze
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On weak center Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 7, Page 489-495, 2001., 2001 Let B be a ring with 1, C the center of B, G a finite automorphism group of B, and BG the set of elements in B fixed under each element in G. Then, the notion of a center Galois extension of BG with Galois group G (i.e., C is a Galois algebra over CG with Galois group G|C≅G) is generalized to a weak center Galois extension with group G, where B is ...
George Szeto, Lianyong Xue
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Fortschritte der Physik, Volume 73, Issue 1-2, February 2025.Abstract S. Gukov and C. Vafa proposed a characterization of rational N=(1,1)$N=(1,1)$ superconformal field theories (SCFTs) in 1+1$1+1$ dimensions with Ricci‐flat Kähler target spaces in terms of the Hodge structure of the target space, extending an earlier observation by G. Moore.
Abhiram Kidambi +2 more
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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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