Modular Diophantine inequalities and some of their invariants. (Q819969)

This paper is devoted to a further study of modular Diophantine inequalities \(ax\bmod b\leq x\). The author describes an algorithm to compute a finite system of generators of the set \(S(a,b)\) of integer solutions of such an inequality. Furthermore, a full affine semigroup \(A(a,b)\) is associated to the numerical semigroup \(S(a,b)\). This provides a method to calculate a minimal system of generators of \(A(a,b)\) and consequently an upper bound for the imbedding dimension of \(S(a,b)\).