151617 20251017144615.0 doi 10.1016/j.jpaa.2021.106773 sideral 126132 ART-2021-126132 eng Elduque, A. Universidad de Zaragoza (orcid)0000-0002-6497-2162 Graded-division algebras and Galois extensions 2021 Access copy available to the general public Unrestricted Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms of central simple graded-division algebras. On the other hand, given a finite abelian group G, any central simple G-graded-division algebra over a field F is determined, thanks to a result of Picco and Platzeck, by its class in the (ordinary) Brauer group of F and the isomorphism class of a G-Galois extension of F. This connection is used to classify the simple G-Galois extensions of F in terms of a Galois field extension L/F with Galois group isomorphic to a quotient G/K and an element in the quotient Z2(K, L×)/B2(K, F×) subject to certain conditions. Non-simple G-Galois extensions are induced from simple T-Galois extensions for a subgroup T of G. We also classify finite-dimensional G-graded-division algebras and, as an application, finite G-graded-division rings. info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-P info:eu-repo/grantAgreement/ES/DGA/E22-17R info:eu-repo/semantics/openAccess by-nc-nd https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 0.834 2021 MATHEMATICS 200 / 333 = 0.601 2021 Q3 T2 MATHEMATICS, APPLIED 220 / 267 = 0.824 2021 Q4 T3 0.866 2021 Algebra and Number Theory 2021 Q1 1.5 2021 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Kochetov, M. 2006 005 Universidad de Zaragoza Dpto. Matemáticas Área Algebra 225, 12 (2021), 106773 [34 pp.] J. pure appl. algebra JOURNAL OF PURE AND APPLIED ALGEBRA 0022-4049 751793 http://zaguan.unizar.es/record/151617/files/texto_completo.pdf Versión publicada 1774626 http://zaguan.unizar.es/record/151617/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:151617 articulos driver 2025-10-17-14:18:54 ARTICLE