Some results in triply–generated telescopic numerical semigroups

Basit Öğe Kaydı
dc.authorid0000-0002-5512-4305en_US
dc.contributor.authorSüer, Meral
dc.contributor.authorİlhan, Sedat
dc.date.accessioned2021-04-26T10:07:59Z
dc.date.available2021-04-26T10:07:59Z
dc.date.issued2017-05en_US
dc.departmentBatman Üniversitesi Fen - Edebiyat Fakültesi Matematik Bölümüen_US
dc.description.abstractIn this study, we assume that ¥ = {0,1,2,...,n,...}, S Í ¥ and ¢ integer set. S is a numerical semigroup if a + b Î S, for a,b Î S , 0Î S and ¥ \S is finite. Let S be a numerical semigroup and X Ì ¥ . X is called minimal system of generators of S if S = < X > and there is not any subset Y Ì X such that S = < Y > . = < > 1 2 3 S s ,s ,s is called a triply-generated telescopic numerical semigroup if Î < > 1 2 3 , s s s d d where = 1 2 d gcd(s s ) (Here, gcd(S)= greatest common divisor the element of S ). Let S be a numerical semigroup, then m(S) = min{x Î S: x > 0} is called as multiplicity of S . The number F(S) = max(¢ \S) is called Frobenius number of S . A numerical semigroup S can be written the form { } - = < > = = = + ® 1 2 0 1 2 1 , ,..., 0, , ,..., , ( ) 1, ... n n n S a a a s s s s s F S , where + < i i 1 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 x Î ¥ and x Ï S , then x is called gap of S . We denote the set of gaps ofS , H(S) = ¥ \S . The number G(S) = #(H(S)) is called the genus ofS . Let S be a numerical semigroup and m Î S ,m> 0. Then Ap(S,m)  x S :x mS is called Apery set of S according to m . Ap(S,m) is formed by the smallest elements of S belonging to the different congruence classes mod m. Thus # (Ap(S,m)) = m and the Frobenius number of S equal to max(Ap(S,m)) - m ( where #(A) stands for Cardinality (A) ). The number n(S) = #({0,1,2,...,F(S)}ÇS) is called determine of numerical semigroup S . Also, It is known that G(S) = F(S)+ 1- n(S) . In this study, we will give some results about gaps, fundamental gaps and the determine number of S triply-generated telescopic numerical semigroups with arbitrary multiplicity.en_US
dc.identifier.citationSüer, M., İlhan, S. (2017). Some results in triply–generated telescopic numerical semigroups. 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/20.500.12402/2993
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.titleSome results in triply–generated telescopic numerical semigroupsen_US
dc.typeConference Objecten_US

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Fen - Edebiyat Fakültesi, Matematik Bölümü, Bildiri Metinleri Koleksiyonu