{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:33:31Z","timestamp":1758710011646},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p>Given two numerical semigroups S and T and a positive integer d, S is said to be one over d of T if S = {s \u2208 \u2115 | ds \u2208 T} and in this case T is called a d-fold of S. We prove that the minimal genus of the d-folds of S is [Formula: see text], where g and f denote the genus and the Frobenius number of S. The case d = 2 is a problem proposed by Robles-P\u00e9rez, Rosales, and Vasco. Furthermore, we find the minimal genus of the symmetric doubles of S and study the particular case when S is almost symmetric. Finally, we study the Frobenius number of the quotient of some families of numerical semigroups.<\/jats:p>","DOI":"10.1142\/s0218196715500290","type":"journal-article","created":{"date-parts":[[2015,7,30]],"date-time":"2015-07-30T02:56:29Z","timestamp":1438224989000},"page":"1043-1053","source":"Crossref","is-referenced-by-count":7,"title":["Minimal genus of a multiple and Frobenius number of a quotient of a numerical semigroup"],"prefix":"10.1142","volume":"25","author":[{"given":"Francesco","family":"Strazzanti","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 degli studi di Pisa, Largo Bruno Pontecorvo 5, Pisa 56127, Italy"}]}],"member":"219","published-online":{"date-parts":[[2015,9,29]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2014.897549"},{"key":"rf2","first-page":"130","volume":"125","author":"Barucci V.","year":"1997","journal-title":"Mem. Amer. Math. Soc."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.6837"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(77)90268-X"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-012-9451-x"},{"key":"rf6","first-page":"15","volume":"33","author":"Delgado M.","year":"2013","journal-title":"CIM Bull."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1080\/00927879408825174"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01273309"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-012-9397-z"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s00013-007-2379-9"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2008.08.005"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2005.03.014"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1080\/00927870802108171"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0160-6"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2003.06.002"},{"key":"rf17","doi-asserted-by":"crossref","unstructured":"I.\u00a0Swanson, Commutative Algebra and its Applications (Walter de Gruyter, Berlin, 2009)\u00a0pp. 383\u2013386.","DOI":"10.1515\/9783110213188.383"},{"key":"rf18","volume":"41","author":"Sylvester J. J.","year":"1884","journal-title":"Educational Times"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196715500290","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T14:45:12Z","timestamp":1652971512000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196715500290"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9]]},"references-count":17,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2015,9,29]]},"published-print":{"date-parts":[[2015,9]]}},"alternative-id":["10.1142\/S0218196715500290"],"URL":"https:\/\/doi.org\/10.1142\/s0218196715500290","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9]]}}}