On Arf closures of some numerical semigroups generated by three elements
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
A 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 ¥ . A numerical semigroup is a set of the form
1, 2 , , 1 2 ... p p S = u u ¼ u = u ¥ + u ¥ + + u ¥ where are positive integers, such that
( ) 1 2 gcd , , , 1 p u u ¼ u = . The condition is saying that S has finite complement in ¥
(where short gcd is the greatest common divisor),( Barucci, Dobbs & Fontana, 1997;
.Fröberg, Gottlieb & Haggkvist, 1987; . Rosales &Garcia-Sanchez, 2009).
If S is a numerical semigroup, then F(S) = max(¢ \S) is called Frobenius
number of S . Any numerical semigroup write this form
{ } 1 2 0 1 2 , ,..., 0 , , ,..., ( ) 1, ... n n S = < a a a > = = s s s s = F S + ® . Where “® ” means that
every integer greater than F(S)+ 1 belongs to the set.
A numerical semigroup S is called Arf if x + y - z Î S for all x, y, z Î S , where
x ³ y ³ z . The smallest Arf numerical semigroup containing a numerical semigroup
S is called the Arf closure of S , and it is denoted by Arf (S) .
Arf numerical semigroup and their applications to algebraic error corerecting
codes have been a special interest in recent times (Brass-Amaros, 2004; Campillo,
Farran & Munuera, 2000). The families of Arf numerical semigroups are related with
the problem solution of singularities in curve.In this presentation, we will give some results between numerical semigroups and theirs Arf closure. Also, we will obtain some relation for Arf closure of these numerical semigroups.
Açıklama
Anahtar Kelimeler
Arf Numerical Semigroup, Arf Closures, Genus
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Süer, M., İlhan, S.,Çelik, A. (2017). On Arf closures of some numerical semigroups generated by three elements. International Conference on Mathematics and Mathematics Education (ICMME-2017), 11-13 Mayıs 2017, Şanlıurfa
