{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T13:04:54Z","timestamp":1767791094468,"version":"3.49.0"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T00:00:00Z","timestamp":1767312000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This work contributes to the study of radical numerical semigroups. If n\u2208Z where n\u22652, then the product of all its prime positive divisors is called the radical of n. It is denoted by r(n). A radical numerical semigroup is a numerical semigroup S such that s+r(s)\u2208S for every s\u2208S\\{0}. We present three algorithms that will help us understand the structure of radical semigroups. These algorithms allow us to calculate all radical numerical semigroups with a fixed genus, with a fixed Frobenius number, as well as with a fixed multiplicity. Furthermore, given X, a set of positive integers such that gcd(X)=1, we will prove the existence of the smallest radical semigroup containing X. We will also present an algorithm to obtain it.<\/jats:p>","DOI":"10.3390\/axioms15010036","type":"journal-article","created":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T11:11:46Z","timestamp":1767352306000},"page":"36","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Radical Numerical Semigroups"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0593-9434","authenticated-orcid":false,"given":"Mar\u00eda \u00c1ngeles","family":"Moreno-Fr\u00edas","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of C\u00e1diz, E-11510 C\u00e1diz, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 C.","family":"Rosales","sequence":"additional","affiliation":[{"name":"Department of Algebra, Faculty of Sciences, University of Granada, E-18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Rosales, J.C., and Garc\u00eda-S\u00e1nchez, P.A. 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