000151617 001__ 151617 000151617 005__ 20250319155217.0 000151617 0247_ $$2doi$$a10.1016/j.jpaa.2021.106773 000151617 0248_ $$2sideral$$a126132 000151617 037__ $$aART-2021-126132 000151617 041__ $$aeng 000151617 100__ $$0(orcid)0000-0002-6497-2162$$aElduque, A.$$uUniversidad de Zaragoza 000151617 245__ $$aGraded-division algebras and Galois extensions 000151617 260__ $$c2021 000151617 5060_ $$aAccess copy available to the general public$$fUnrestricted 000151617 5203_ $$aGraded-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. 000151617 536__ $$9info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-P$$9info:eu-repo/grantAgreement/ES/DGA/E22-17R 000151617 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000151617 590__ $$a0.834$$b2021 000151617 591__ $$aMATHEMATICS$$b200 / 333 = 0.601$$c2021$$dQ3$$eT2 000151617 591__ $$aMATHEMATICS, APPLIED$$b220 / 267 = 0.824$$c2021$$dQ4$$eT3 000151617 592__ $$a0.866$$b2021 000151617 593__ $$aAlgebra and Number Theory$$c2021$$dQ1 000151617 594__ $$a1.5$$b2021 000151617 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000151617 700__ $$aKochetov, M. 000151617 7102_ $$12006$$2005$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Algebra 000151617 773__ $$g225, 12 (2021), 106773 [34 pp.]$$pJ. pure appl. algebra$$tJOURNAL OF PURE AND APPLIED ALGEBRA$$x0022-4049 000151617 8564_ $$s751793$$uhttps://zaguan.unizar.es/record/151617/files/texto_completo.pdf$$yVersión publicada 000151617 8564_ $$s1774626$$uhttps://zaguan.unizar.es/record/151617/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000151617 909CO $$ooai:zaguan.unizar.es:151617$$particulos$$pdriver 000151617 951__ $$a2025-03-19-14:19:17 000151617 980__ $$aARTICLE