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Proportionally modular Diophantine inequalities. (English) Zbl 1039.20036
The authors study the sets of nonnegative solutions of Diophantine inequalities of the form $$ax$$ mod $$b \leq cx$$ with $$a, b$$ and $$c$$ positive integers. These sets are numerical semigroups, which are investigated and characterized.

##### MSC:
 20M14 Commutative semigroups 11D75 Diophantine inequalities
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##### References:
 [1] Garcı́a-Sánchez, P.A.; Rosales, J.C., Numerical semigroups generated by intervals, Pacific J. math., 191, 1, 75-83, (1999) · Zbl 1009.20069 [2] Rosales, J.C.; Branco, M.B., Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups, J. pure appl. algebra, 171, 303-314, (2002) · Zbl 1006.20043 [3] Rosales, J.C.; Branco, M.B., Decomposition of a numerical semigroup as an intersection of irreducible numerical semigroups, B. belg. math. soc-sim., 9, 372-381, (2002) · Zbl 1051.20027 [4] Rosales, J.C.; Branco, M.B., Irreducible numerical semigroups, Pacific J. math., 209, 131-143, (2003) · Zbl 1057.20042 [5] J.C. Rosales, P.A. Garcı́a-Sanchez, J.M. Urbano-Blanco, Modular Diophantine inequalities and numerical semigroups, Pacific J. Math., to appear. · Zbl 1184.20052
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