Opened modular numerical semigroups

[摘要] We introduce the class of the opened modular numerical semigroups (for brevity, OM-semigroups) and obtain formulas for the Frobenius number, the singularity degree and the type of these semigroups. We prove that a numerical semigroup S has a Toms decomposition if and only if S is an intersection of OM-semigroups. We also characterize irreducible proportionally modular numerical semigroups in terms of OM-semigroups. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] modular diophantine inequality;numerical semigroup;Frobenius number