{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:08:38Z","timestamp":1753880918519,"version":"3.41.2"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","funder":[{"DOI":"10.13039\/501100004410","name":"TUBITAK","doi-asserted-by":"crossref","award":["122F130"],"award-info":[{"award-number":["122F130"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"crossref"}]},{"name":"FCT - Funda\u00e7\u00e3ao para aCi\u00eancia e a Technologia, I.P.,","award":["UIDB\/00144\/2020","UIDP\/00144\/2020"],"award-info":[{"award-number":["UIDB\/00144\/2020","UIDP\/00144\/2020"]}]},{"DOI":"10.13039\/501100004410","name":"TUBITAK","doi-asserted-by":"crossref","award":["122F158"],"award-info":[{"award-number":["122F158"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p> It is well known that a ring [Formula: see text] is right Kasch if each simple right [Formula: see text]-module embeds in a projective right [Formula: see text]-module. In this paper we study the dual notion and call a ring [Formula: see text] right dual Kasch if each simple right [Formula: see text]-module is a homomorphic image of an injective right [Formula: see text]-module. We prove that [Formula: see text] is right dual Kasch if and only if every finitely generated projective right [Formula: see text]-module is coclosed in its injective hull. Typical examples of dual Kasch rings are self-injective rings, V-rings and commutative perfect rings. Skew group rings of dual Kasch rings by finite groups are dual Kasch if the order of the group is invertible. Many examples are given to separate the notion of Kasch and dual Kasch rings. It is shown that commutative Kasch rings are dual Kasch, and a commutative ring with finite Goldie dimension is dual Kasch if and only if it is a classical ring (i.e. every element is a zero divisor or invertible). We obtain that, for a field [Formula: see text], a finite dimensional [Formula: see text]-algebra is right dual Kasch if and only if it is left Kasch. We also discuss the rings over which every simple right module is a homomorphic image of its injective hull, and these rings are termed strongly dual Kasch. <\/jats:p>","DOI":"10.1142\/s0219498824502256","type":"journal-article","created":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T17:41:09Z","timestamp":1686073269000},"source":"Crossref","is-referenced-by-count":2,"title":["Dual Kasch rings"],"prefix":"10.1142","volume":"23","author":[{"given":"Engin","family":"B\u00fcy\u00fcka\u015f\u0131k","sequence":"first","affiliation":[{"name":"Izmir Institute of Technology, Department of Mathematics, 35430, Urla, Izmir, Turkey"}]},{"given":"Christian","family":"Lomp","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica da Universidade do Porto, Faculdade de Ci\u00eancias, Universidade do Porto Rua Campo Alegre, 687, 4169-007 Porto, Portugal"}]},{"given":"Haydar Baran","family":"Yurtsever","sequence":"additional","affiliation":[{"name":"Izmir Institute of Technology, Department of Mathematics, 35430, Urla, Izmir, Turkey"}]}],"member":"219","published-online":{"date-parts":[[2023,7,10]]},"reference":[{"key":"S0219498824502256BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S021949882150095X"},{"key":"S0219498824502256BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9913-1"},{"key":"S0219498824502256BIB003","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511614309"},{"key":"S0219498824502256BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623608"},{"key":"S0219498824502256BIB005","doi-asserted-by":"publisher","DOI":"10.4134\/JKMS.2014.51.6.1305"},{"key":"S0219498824502256BIB006","doi-asserted-by":"publisher","DOI":"10.1080\/00927877808822299"},{"key":"S0219498824502256BIB007","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1963-067-0"},{"key":"S0219498824502256BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s40065-012-0003-8"},{"key":"S0219498824502256BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01222535"},{"key":"S0219498824502256BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01361137"},{"key":"S0219498824502256BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0525-8"},{"key":"S0219498824502256BIB012","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/030"},{"key":"S0219498824502256BIB013","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546525"},{"key":"S0219498824502256BIB014","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-1983-13-1-37"},{"key":"S0219498824502256BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2021.01.040"},{"key":"S0219498824502256BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-018-0860-5"},{"key":"S0219498824502256BIB017","volume-title":"Foundations of Module and Ring Theory","volume":"3","author":"Wisbauer R.","year":"1991"}],"container-title":["Journal of Algebra and Its Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219498824502256","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,5]],"date-time":"2024-11-05T04:10:05Z","timestamp":1730779805000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219498824502256"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,10]]},"references-count":17,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["10.1142\/S0219498824502256"],"URL":"https:\/\/doi.org\/10.1142\/s0219498824502256","relation":{},"ISSN":["0219-4988","1793-6829"],"issn-type":[{"type":"print","value":"0219-4988"},{"type":"electronic","value":"1793-6829"}],"subject":[],"published":{"date-parts":[[2023,7,10]]},"article-number":"2450225"}}