{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T19:55:34Z","timestamp":1694634934038},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,3]]},"abstract":"<jats:p>Let \u2115 be the set of nonnegative integers and let I be an interval of positive rational numbers. Then [Formula: see text] is a numerical semigroup. In this paper we study the multiplicity of the numerical semigroups of the form [Formula: see text], where a and b are integers such that 2 \u2264 a &lt; b. We also see the connection between the multiplicity and the Frobenius number of this type of semigroups.<\/jats:p>","DOI":"10.1142\/s0218196709005056","type":"journal-article","created":{"date-parts":[[2009,3,27]],"date-time":"2009-03-27T11:19:21Z","timestamp":1238152761000},"page":"235-246","source":"Crossref","is-referenced-by-count":2,"title":["OPENED MODULAR NUMERICAL SEMIGROUPS WITH A GIVEN MULTIPLICITY"],"prefix":"10.1142","volume":"19","author":[{"given":"J. C.","family":"ROSALES","sequence":"first","affiliation":[{"name":"Departamento de \u00c1lgebra, Universidad de Granada, E-18071 Granada, Spain"}]},{"given":"P.","family":"VASCO","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade de Tr\u00e1s-os-Montes e Alto, Douro, 5001-801 Vila Real, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"1198","volume":"222","author":"Ap\u00e9ry R.","journal-title":"C. R. Acad. Sci. Paris"},{"key":"rf2","volume":"598","author":"Barucci V.","journal-title":"Memoirs of the Amer. Math. Soc."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-08-02173-X"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198568209.001.0001"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2005.03.014"},{"key":"rf6","volume-title":"Finitely Generated Commutative Monoids","author":"Rosales J. C.","year":"1999"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2003.06.002"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.08.009"},{"key":"rf9","doi-asserted-by":"crossref","first-page":"367","DOI":"10.21136\/MB.2008.140626","volume":"133","author":"Rosales J. C.","journal-title":"Math. Bohemica"},{"key":"rf10","first-page":"203","volume":"11","author":"Rosales J. C.","journal-title":"Math. Inequal. Appl."},{"key":"rf11","first-page":"1","volume":"294","author":"Selmer E. S.","journal-title":"J. Reine Angew. Math."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005056","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,3]],"date-time":"2021-10-03T17:47:11Z","timestamp":1633283231000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005056"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3]]},"references-count":11,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,3]]}},"alternative-id":["10.1142\/S0218196709005056"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005056","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3]]}}}