{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:44:35Z","timestamp":1740120275330,"version":"3.37.3"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100005033","name":"Bialystok University of Technology","doi-asserted-by":"crossref","award":["WZ\/WIIIT\/1\/2020"],"award-info":[{"award-number":["WZ\/WIIIT\/1\/2020"]}],"id":[{"id":"10.13039\/501100005033","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:p>We prove that if a ring [Formula: see text] is a sum of its Jacobson radical subring [Formula: see text] and additive subgroup [Formula: see text] with [Formula: see text], then the ring [Formula: see text] is Jacobson radical, which answers a question asked by Kelarev and McConnell. Using this result we also show that for a semigroup [Formula: see text] the class of Jacobson radical rings is [Formula: see text]-sum closed if and only if [Formula: see text] is locally finite and all subgroups of [Formula: see text] are [Formula: see text]-groups.<\/jats:p>","DOI":"10.1142\/s0218196722500515","type":"journal-article","created":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T14:20:48Z","timestamp":1653056448000},"page":"1203-1208","source":"Crossref","is-referenced-by-count":2,"title":["On rings which are sums of subrings and additive subgroups"],"prefix":"10.1142","volume":"32","author":[{"given":"Marek","family":"K\u0229pczyk","sequence":"first","affiliation":[{"name":"Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15\u2013351 Bia\u0142ystok, Poland"}]}],"member":"219","published-online":{"date-parts":[[2022,6,21]]},"reference":[{"key":"S0218196722500515BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02844841"},{"key":"S0218196722500515BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF00750549"},{"key":"S0218196722500515BIB004","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2003.209.17"},{"key":"S0218196722500515BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BF01194866"},{"key":"S0218196722500515BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01470877"},{"key":"S0218196722500515BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(64)90026-2"},{"key":"S0218196722500515BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573766"},{"key":"S0218196722500515BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01202307"},{"key":"S0218196722500515BIB010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-04169-5"},{"key":"S0218196722500515BIB011","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1998-012-5"},{"key":"S0218196722500515BIB012","volume-title":"Ring Constructions and Applications","volume":"9","author":"Kelarev A. 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