On Arf closures of some numerical semigroups generated by three elements

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dc.authorid0000-0002-5512-4305en_US
dc.contributor.authorSüer, Meral
dc.contributor.authorİlhan, Sedat
dc.contributor.authorÇelik, Ahmet
dc.date.accessioned2021-04-26T10:17:27Z
dc.date.available2021-04-26T10:17:27Z
dc.date.issued2017-05en_US
dc.departmentBatman Üniversitesi Fen - Edebiyat Fakültesi Matematik Bölümüen_US
dc.description.abstractA numerical semigroup is a subset of the set of nonnegative integers (denoted here by ¥ ) closed under addition, containing the zero element and with finite complement in ¥ . A numerical semigroup is a set of the form 1, 2 , , 1 2 ... p p S = u u ¼ u = u ¥ + u ¥ + + u ¥ where are positive integers, such that ( ) 1 2 gcd , , , 1 p u u ¼ u = . The condition is saying that S has finite complement in ¥ (where short gcd is the greatest common divisor),( Barucci, Dobbs & Fontana, 1997; .Fröberg, Gottlieb & Haggkvist, 1987; . Rosales &Garcia-Sanchez, 2009). If S is a numerical semigroup, then F(S) = max(¢ \S) is called Frobenius number of S . Any numerical semigroup write this form { } 1 2 0 1 2 , ,..., 0 , , ,..., ( ) 1, ... n n S = < a a a > = = s s s s = F S + ® . Where “® ” means that every integer greater than F(S)+ 1 belongs to the set. A numerical semigroup S is called Arf if x + y - z Î S for all x, y, z Î S , where x ³ y ³ z . The smallest Arf numerical semigroup containing a numerical semigroup S is called the Arf closure of S , and it is denoted by Arf (S) . Arf numerical semigroup and their applications to algebraic error corerecting codes have been a special interest in recent times (Brass-Amaros, 2004; Campillo, Farran & Munuera, 2000). The families of Arf numerical semigroups are related with the problem solution of singularities in curve.In this presentation, we will give some results between numerical semigroups and theirs Arf closure. Also, we will obtain some relation for Arf closure of these numerical semigroups.en_US
dc.identifier.citationSüer, M., İlhan, S.,Çelik, A. (2017). On Arf closures of some numerical semigroups generated by three elements. International Conference on Mathematics and Mathematics Education (ICMME-2017), 11-13 Mayıs 2017, Şanlıurfaen_US
dc.identifier.urihttp://theicmme.org/2017/Default.aspx
dc.identifier.urihttps://hdl.handle.net/20.500.12402/2994
dc.language.isoenen_US
dc.publisherHarran Üniversitesien_US
dc.relation.journalInternational Conference on Mathematics and Mathematics Education (ICMME-2017), 11-13 Mayıs 2017en_US
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectArf Numerical Semigroupen_US
dc.subjectArf Closuresen_US
dc.subjectGenusen_US
dc.titleOn Arf closures of some numerical semigroups generated by three elementsen_US
dc.typeConference Objecten_US

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Fen - Edebiyat Fakültesi, Matematik Bölümü, Bildiri Metinleri Koleksiyonu