doi:10.1016/j.jpaa.2021.106773engElduque, A.Kochetov, M.Graded-division algebras and Galois extensionsART-2021-126132Graded-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.2021http://zaguan.unizar.es/record/15161710.1016/j.jpaa.2021.106773http://zaguan.unizar.es/record/151617oai:zaguan.unizar.es:151617info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-Pinfo:eu-repo/grantAgreement/ES/DGA/E22-17RJOURNAL OF PURE AND APPLIED ALGEBRA 225, 12 (2021), 106773 [34 pp.]by-nc-ndhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.esinfo:eu-repo/semantics/openAccess