Frobenius Numbers Of Numerical Semigroup Quotient

Numerical semigroups,as a special kind of monoids,have many applications in other fields of algebra.After Urbano-blanco et al.studied the diophantine inequality,it was proved that the nonnegative solution set of diophantine inequality is a numerical semigroup.They call this kind of numerical semigroup as proportional modulus word semigroup,and it is precisely to describe the concept of proportional modulus word semigroup that they put forward the concept of quotient of numerical semigroup.In this paper,through the theoretical research of the number semigroup by J.C.Rosales,the quotient of the number semigroup and some typical Numbers of the number semigroup are summarized and studied.In reference on the basis of a large number of literature,d-symmetric numerical semigroup,for example,through to the numerical semigroup and proportion module word semigroup research,as well as for some typical numerical semigroup,calculation formula of number,and some related conclusions and formulas,and by using these conclusions and formula,in symmetric numerical semigroup is extended.In addition,some formulas and their corollaries about the quotient of d-symmetric numerical semigroups are proved.Finally,it summarizes the expression of numerical semigroup under different values of d(prime number).Finally,I guess if d is composite,I can give the corresponding expression.