On the numerical semigroups with generated by two elements with multiplicity 3
Küçük Resim Yok
Tarih
2017-05
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Harran Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Attribution-NonCommercial-ShareAlike 3.0 United States
Attribution-NonCommercial-ShareAlike 3.0 United States
Özet
Throughout 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) xS :x mS
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 .
Açıklama
Anahtar Kelimeler
Frobenius Number, Telescopic Numerical Semigroup, Genus
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
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
