Some results on Arf numerical semigroups with multiplicity 8

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dc.authorid0000-0002-5512-4305en_US
dc.contributor.authorSüer, Meral
dc.contributor.authorİlhan, Sedat
dc.date.accessioned2021-04-26T08:51:37Z
dc.date.available2021-04-26T08:51:37Z
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 ¥ . Note also that up to isomorphism the set of numerical semigroups classify the set of all submonoids of ( , ) ¥ + . Let S be submonoid of ¥ , the condition of having finite complement in ¥ is equivalent to saying that the greatest common divisor (gcd for short) of its elements is one. Those positive integers which do not belong to S are called gaps of S . The number of gaps of S is called the genus of S and it is denoted by G S( ) . The largest gaps of S is F S( ) if S is different from ¥ . m S s S s ( ) min : 0 = Î > { } are called multiplicity of S , respectively. Also, n S Card F S S ( ) 0,1,2,..., ( ) = Ç ({ } ) is called the number determine of S . If a Î ¥ and a S Ï , 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 known that G S F S n S ( ) ( ) 1 ( ) = + - . A numerical semigroup S is called Arf if x y z S + - Î for all x y z S , , Î , where x y z ³ ³ . This definition was first given by C. Arf in 1949. In the study, we intend to examine the Arf numerical semigroup with multiplicity eight and fixed conductor. We will also able to compute the notable elements and special sets of these numerical semigroups.en_US
dc.identifier.citationSüer, M., İlhan, S. (2017). Some results on Arf numerical semigroups with multiplicity 8. 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/20.500.12402/2986
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/restrictedAccessen_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectArf Numerical Semigroupsen_US
dc.subjectPseudo-Frobenius Numberen_US
dc.subjectGenusen_US
dc.titleSome results on Arf numerical semigroups with multiplicity 8en_US
dc.typeConference Objecten_US

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Fen - Edebiyat Fakültesi, Matematik Bölümü, Bildiri Metinleri Koleksiyonu