On the numerical semigroups with generated by two elements with multiplicity 3

Basit Öğe Kaydı
dc.authorid0000-0002-5512-4305en_US
dc.contributor.authorSüer, Meral
dc.contributor.authorİlhan, Sedat
dc.contributor.authorÇelik, Ahmet
dc.date.accessioned2021-04-26T11:13:55Z
dc.date.available2021-04-26T11:13:55Z
dc.date.issued2017-05en_US
dc.departmentBatman Üniversitesi Fen - Edebiyat Fakültesi Matematik Bölümüen_US
dc.description.abstractThroughout this study, we assume that ¥ and ¢ be the sets of nonnegative integers and integers, respectively. The subset S of ¥ is a numerical semigroup if 0 Î S , x + y Î S, for all x, y Î S , and Card(¥ \S)< ¥ ( this condition is equivalent to gcd(S)= 1 , gcd(S)= greatest common divisor the element of S ) . Let S be a numerical semigroup, then F(S) = max(¢ \S) and m(S) = min{s Î S: s > 0} are called Frobenius number and multiplicity of S , respectively. Also, n(S) = Card ({0,1,2,...,F(S)}ÇS)is called the number determine of S . If S is a numerical semigroup such that 1 2 , ,..., r S = < a a a > , then we observe that { } 1 2 0 , 2 1 , ,..., 0, , ,..., , ( ) 1, ... r n n S a a a s s s s s F S - = < > = = = + ® where 1 , ( ) i i s s n n S + < = , and the arrow means that every integer greater than F(S) + 1 belongs to S , for i = 1,2,...,n = n(S) . If a Î ¥ and a Ï S , then a is called gap of S . We denote the set of gaps of S , by H(S) , i.e, H(S) = ¥ \S .The G(S) = Card(H(S)) is called the genus of S . Also, It is known that G(S) = F(S) + 1- n(S) . Let S be a numerical semigroup andm Î S ,m > 0 . Then Ap(S,m)  xS :x mS  is called Apery set of S according to m . A numerical semigroup S is Arf if a+ b- c Î S , for all a,b,c Î S such that a ³ b ³ c. The intersection of any family of Arf numerical semigroups is again an Arf numerical semigroup. Thus, since ¥ is an Arf numerical semigroup, one can consider the smallest Arf numerical semigroup containing a given numerical semigroup. The smallest Arf numerical semigroup containing a numerical semigroup S is called the Arf closure of S , and it is denoted by Arf (S) . In this presentation, we will give some results about gaps, the determine number, Apery set and Arf closure of S numerical semigroup such that S = 3, x .en_US
dc.identifier.citationSüer, M., İlhan, S.,Çelik, A. (2017). On the numerical semigroups with generated by two elements with multiplicity 3. 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/20.500.12402/2999
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.subjectFrobenius Numberen_US
dc.subjectTelescopic Numerical Semigroupen_US
dc.subjectGenusen_US
dc.titleOn the numerical semigroups with generated by two elements with multiplicity 3en_US
dc.typeConference Objecten_US

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Koleksiyon

Fen - Edebiyat Fakültesi, Matematik Bölümü, Bildiri Metinleri Koleksiyonu