论文标题
几乎规范的理想和气体数值半群
Almost canonical ideals and GAS numerical semigroups
论文作者
论文摘要
我们提出了气体数值半群的概念，该概念概括了几乎对称和2-AGL数值半群。此外，我们介绍了几乎规范理想的概念，该概念以几乎对称的数字半群的相同方式推广了规范理想的概念。我们证明，当$ m-e $是$ m-m $的几乎规范的理想时，只有$ m-m $的数字$ m $ and $ e $是$ m $的数值半群，而倍数$ e $ is is as as as as as as as as as Gas。这概括了Barucci关于几乎对称的半群和Chau，Goto，Kumashiro和Matsuoka的定理的结果。我们还研究了气体从数值半群的转移到其胶合，数值重复和扩张。
We propose the notion of GAS numerical semigroup which generalizes both almost symmetric and 2-AGL numerical semigroups. Moreover, we introduce the concept of almost canonical ideal which generalizes the notion of canonical ideal in the same way almost symmetric numerical semigroups generalize symmetric ones. We prove that a numerical semigroup with maximal ideal $M$ and multiplicity $e$ is GAS if and only if $M-e$ is an almost canonical ideal of $M-M$. This generalizes a result of Barucci about almost symmetric semigroups and a theorem of Chau, Goto, Kumashiro, and Matsuoka about 2-AGL semigroups. We also study the transfer of the GAS property from a numerical semigroup to its gluing, numerical duplication and dilatation.
