{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T20:44:22Z","timestamp":1776113062181,"version":"3.50.1"},"reference-count":2,"publisher":"American Mathematical Society (AMS)","issue":"2","license":[{"start":{"date-parts":[[2008,10,25]],"date-time":"2008-10-25T00:00:00Z","timestamp":1224892800000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>\n                    Let\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S\">\n                        <mml:semantics>\n                          <mml:mi>S<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">S<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    be a numerical semigroup. Then there exists a symmetric numerical semigroup\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S overbar\">\n                        <mml:semantics>\n                          <mml:mover>\n                            <mml:mi>S<\/mml:mi>\n                            <mml:mo accent=\"false\">\n                              \u00af\n                              \n                            <\/mml:mo>\n                          <\/mml:mover>\n                          <mml:annotation encoding=\"application\/x-tex\">\\overline {S}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    such that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S equals StartSet n element-of double-struck upper N vertical-bar 2 n element-of upper S overbar EndSet\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>S<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mo fence=\"false\" stretchy=\"false\">{<\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u2208\n                              \n                            <\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">N<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mtext>\u00a0<\/mml:mtext>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mtext>\u00a0<\/mml:mtext>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u2208\n                              \n                            <\/mml:mo>\n                            <mml:mover>\n                              <mml:mi>S<\/mml:mi>\n                              <mml:mo accent=\"false\">\n                                \u00af\n                                \n                              <\/mml:mo>\n                            <\/mml:mover>\n                            <mml:mo fence=\"false\" stretchy=\"false\">}<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">S=\\{ n\\in \\mathbb {N} ~|~ 2n \\in \\overline {S}\\}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0002-9939-07-09098-3","type":"journal-article","created":{"date-parts":[[2007,12,10]],"date-time":"2007-12-10T11:54:12Z","timestamp":1197287652000},"page":"475-477","source":"Crossref","is-referenced-by-count":9,"special_numbering":"584","title":["Every numerical semigroup is one half of a symmetric numerical semigroup"],"prefix":"10.1090","volume":"136","author":[{"given":"J.","family":"Rosales","sequence":"first","affiliation":[]},{"given":"P.","family":"Garc\u00eda-S\u00e1nchez","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2007,10,25]]},"reference":[{"key":"1","series-title":"Oxford Lecture Series in Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198568209.001.0001","volume-title":"The Diophantine Frobenius problem","volume":"30","author":"Ram\u00edrez Alfons\u00edn, J. L.","year":"2005","ISBN":"https:\/\/id.crossref.org\/isbn\/9780198568209"},{"key":"2","doi-asserted-by":"publisher","first-page":"748","DOI":"10.2307\/2036742","article-title":"The value-semigroup of a one-dimensional Gorenstein ring","volume":"25","author":"Kunz, Ernst","year":"1970","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"}],"container-title":["Proceedings of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/proc\/2008-136-02\/S0002-9939-07-09098-3\/S0002-9939-07-09098-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/proc\/2008-136-02\/S0002-9939-07-09098-3\/S0002-9939-07-09098-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T19:28:23Z","timestamp":1776108503000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/proc\/2008-136-02\/S0002-9939-07-09098-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,10,25]]},"references-count":2,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["S0002-9939-07-09098-3"],"URL":"https:\/\/doi.org\/10.1090\/s0002-9939-07-09098-3","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6826","0002-9939"],"issn-type":[{"value":"1088-6826","type":"electronic"},{"value":"0002-9939","type":"print"}],"subject":[],"published":{"date-parts":[[2007,10,25]]}}}