caa a22 4500 445344857 CHVBK 20180317142825.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00233-010-9275-5 doi (NATIONALLICENCE)springer-10.1007/s00233-010-9275-5 Numerical semigroups whose fractions are of maximal embedding dimension [Elektronische Daten] [David Dobbs, Harold Smith] Each saturated (resp., Arf) numerical semigroup S has the property that each of its fractions $\frac{S}{k}$ is saturated (resp., Arf), but the property of being of maximal embedding dimension (MED) is not stable under formation of fractions. If S is a numerical semigroup, then S is MED (resp., Arf; resp., saturated) if and only if, for each 2≤k∈ℕ, $S = \frac{T}{k}$ for infinitely many MED (resp., Arf; resp., saturated) numerical semigroups T. Let $\mathcal{A}$ (resp., $\mathcal{F}$) be the class of Arf numerical semigroups (resp., of numerical semigroups each of whose fractions is of maximal embedding dimension). Then there exists an infinite strictly ascending chain $\mathcal{A} =\mathcal{C}_{1} \subset\mathcal{C}_{2} \subset\mathcal{C}_{3}\subset \,\cdots\, \subset\mathcal{F}$, where, like $\mathcal{A}$ and $\mathcal{F}$, each $\mathcal{C}_{n}$ is stable under the formation of fractions. Springer Science+Business Media, LLC, 2010 Numerical semigroup nationallicence Maximal embedding dimension nationallicence Arf numerical semigroup nationallicence Saturated numerical semigroup nationallicence Multiplicity nationallicence Frobenius number nationallicence Fractionally closed nationallicence Dobbs David Department of Mathematics, University of Tennessee, 37996-0614, Knoxville, TN, USA aut Smith Harold Department of Mathematics and Physics, Thomas More College, 41017, Crestview Hills, KY, USA aut Semigroup Forum Springer-Verlag 82/3(2011-06-01), 412-422 0037-1912 82:3<412 2011 82 233 https://doi.org/10.1007/s00233-010-9275-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-010-9275-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dobbs David Department of Mathematics, University of Tennessee, 37996-0614, Knoxville, TN, USA aut NATIONALLICENCE 700 1- Smith Harold Department of Mathematics and Physics, Thomas More College, 41017, Crestview Hills, KY, USA aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 82/3(2011-06-01), 412-422 0037-1912 82:3<412 2011 82 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer