{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:01:08Z","timestamp":1758279668548,"version":"3.37.3"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology of Taiwan","doi-asserted-by":"crossref","award":["MOST 110-2115-M-005-004-MY2"],"award-info":[{"award-number":["MOST 110-2115-M-005-004-MY2"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> Let [Formula: see text] be a ring with a partial action [Formula: see text] of a finite group [Formula: see text]. We determine when a quotient group of [Formula: see text] gives rise to a partial action induced by [Formula: see text] on a subring of [Formula: see text]. As an application, we show that if [Formula: see text] is an [Formula: see text]-partial Galois extension and [Formula: see text] is a normal subgroup of [Formula: see text], then under certain conditions [Formula: see text] under the partial action of [Formula: see text] induced by [Formula: see text], denoted by [Formula: see text], is a partial Galois extension. This result was just shown recently by Bagio et al., applying globalization to derive a partial action of [Formula: see text] on [Formula: see text], totally different from the one presented in this paper arising from a Boolean ring generated by certain idempotents. We further show in either type of induced partial action of a quotient group that under certain conditions [Formula: see text] is a DeMeyer\u2013Kanzaki [Formula: see text]-partial Galois extension whenever [Formula: see text] is an [Formula: see text]-partial Galois Azumaya extension. A structure theorem for a partial Galois extension is also presented, namely, every partial Galois extension can be decomposed as a direct sum of Galois extensions and possibly a trivial partial Galois extension of type II. <\/jats:p>","DOI":"10.1142\/s0218196723500431","type":"journal-article","created":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T06:10:40Z","timestamp":1687155040000},"page":"989-1006","source":"Crossref","is-referenced-by-count":3,"title":["On the induced partial action of a quotient group and a structure theorem for a partial Galois extension"],"prefix":"10.1142","volume":"33","author":[{"given":"Jung-Miao","family":"Kuo","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, National Chung Hsing University, Taichung 402, Taiwan"}]},{"given":"George","family":"Szeto","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bradley University, Peoria, IL 61625, USA"}]}],"member":"219","published-online":{"date-parts":[[2023,7,27]]},"reference":[{"key":"S0218196723500431BIB001","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1080\/00927872.2021.1984495","volume":"50","author":"Bagio D.","year":"2022","journal-title":"Commun. 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Math."},{"key":"S0218196723500431BIB007","doi-asserted-by":"crossref","first-page":"2150004","DOI":"10.1142\/S0219498821500043","volume":"19","author":"Jiang X.","year":"2020","journal-title":"J. Algebra Appl."},{"key":"S0218196723500431BIB008","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1007\/s00605-013-0591-1","volume":"175","author":"Kuo J.-M.","year":"2014","journal-title":"Monatsh Math."},{"key":"S0218196723500431BIB009","doi-asserted-by":"crossref","first-page":"1650061","DOI":"10.1142\/S0219498816500614","volume":"15","author":"Kuo J.-M.","year":"2016","journal-title":"J. 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