Rosales, J. C. Modular Diophantine inequalities and some of their invariants. (English) Zbl 1094.20037 Indian J. Pure Appl. Math. 36, No. 8, 417-429 (2005). 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 \(S(a,b)\). Reviewer: Robert F. Tichy (Graz) MSC: 20M14 Commutative semigroups 11D75 Diophantine inequalities 20M05 Free semigroups, generators and relations, word problems Keywords:modular Diophantine inequalities; algorithms; finite systems of generators; full affine semigroups; numerical semigroups; imbedding dimension; Apéry sets; Frobenius numbers PDFBibTeX XMLCite \textit{J. C. Rosales}, Indian J. Pure Appl. Math. 36, No. 8, 417--429 (2005; Zbl 1094.20037)