dc.contributor.author Süer, Meral dc.contributor.author İlhan, Sedat dc.contributor.author Çelik, Ahmet dc.date.accessioned 2021-04-26T11:13:55Z dc.date.available 2021-04-26T11:13:55Z dc.date.issued 2017-05 en_US dc.identifier.citation Süer, 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, Şanlıurfa en_US dc.identifier.uri http://theicmme.org/2017/Default.aspx dc.identifier.uri https://hdl.handle.net/20.500.12402/2999 dc.description.abstract Throughout this study, we assume that ¥ and ¢ be the sets of nonnegative en_US 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 . dc.language.iso eng en_US dc.publisher Harran Üniversitesi en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights Attribution-NonCommercial-ShareAlike 3.0 United States * dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/us/ * dc.subject Frobenius Number en_US dc.subject Telescopic Numerical Semigroup en_US dc.subject Genus en_US dc.title On the numerical semigroups with generated by two elements with multiplicity 3 en_US dc.type conferenceObject en_US dc.relation.journal International Conference on Mathematics and Mathematics Education (ICMME-2017), 11-13 Mayıs 2017 en_US dc.contributor.department Batman Üniversitesi Fen - Edebiyat Fakültesi Matematik Bölümü en_US dc.contributor.authorID 0000-0002-5512-4305 en_US dc.relation.publicationcategory Konferans Öğesi - Uluslararası - Kurum Öğretim Elemanı en_US
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