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In this paper, we study this question in the realm of numerical semigroup rings and, up to multiplicity 9, completely classify which of these rings possess a nontrivial semidualizing module. Using this classification, for each integer [Formula: see text], we construct a numerical semigroup ring of multiplicity n which admits a nontrivial semidualizing module. <\/jats:p>","DOI":"10.1142\/s0218196724500218","type":"journal-article","created":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T03:53:36Z","timestamp":1713498816000},"page":"607-637","source":"Crossref","is-referenced-by-count":1,"title":["Semidualizing modules over numerical semigroup rings"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7304-9089","authenticated-orcid":false,"given":"Ela","family":"Celikbas","sequence":"first","affiliation":[{"name":"School of Mathematical and Data Sciences, West Virginia University, Morgantown, WV 26506, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4012-6404","authenticated-orcid":false,"given":"Hugh","family":"Geller","sequence":"additional","affiliation":[{"name":"School of Mathematical and Data Sciences, West Virginia University, Morgantown, WV 26506, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1294-8144","authenticated-orcid":false,"given":"Toshinori","family":"Kobayashi","sequence":"additional","affiliation":[{"name":"School of Science and Technology, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,6,19]]},"reference":[{"key":"S0218196724500218BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498816500973"},{"key":"S0218196724500218BIB002","doi-asserted-by":"publisher","DOI":"10.24033\/msmf.339"},{"key":"S0218196724500218BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2022.07.027"},{"key":"S0218196724500218BIB004","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-14311"},{"key":"S0218196724500218BIB005","doi-asserted-by":"crossref","unstructured":"W. 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