{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:30:56Z","timestamp":1760059856326,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T00:00:00Z","timestamp":1752624000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004410","name":"Scientific and Technological Research Council of T\u00fcrkiye (TUBITAK)","doi-asserted-by":"publisher","award":["122F130"],"award-info":[{"award-number":["122F130"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Recently, the concept of subprojectivity domains for modules has been introduced as a means of quantifying the level of projectivity exhibited by a module. In this research article, we focus on the subprojectivity domain of Goldie torsion modules. In particular, we establish that a ring denoted as R is classified as right nonsingular if and only if the subprojectivity domain of each Goldie torsion module is closed under submodules. In addition, we demonstrate that a right C-ring is a right nonsingular ring if and only if every module possesses an epic ecf-flat envelope, which is further equivalent to each Goldie torsion module having an epic projective envelope.<\/jats:p>","DOI":"10.3390\/axioms14070536","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T15:48:22Z","timestamp":1752680902000},"page":"536","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Subprojectivity of Goldie Torsion Modules"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3871-217X","authenticated-orcid":false,"given":"Hashem","family":"Bordbar","sequence":"first","affiliation":[{"name":"Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1230-8964","authenticated-orcid":false,"given":"Y\u0131lmaz","family":"Dur\u011fun","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u00c7ukurova University, Adana 01330, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5466-2880","authenticated-orcid":false,"given":"Yara","family":"\u015eihkayad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u00c7ukurova University, Adana 01330, T\u00fcrkiye"}]},{"given":"Erg\u00fcl","family":"T\u00fcrkmen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amasya University, Amasya 05100, T\u00fcrkiye"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Enochs, E.E., and Jenda, O.M.G. 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