Abstract

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.

摘要

我们提出了 GAS 数值半群的概念，它概括了几乎对称和 2-AGL 数值半群。此外，我们引入了近似正则理想的概念，它以几乎对称数值半群推广对称半群的相同方式推广了正则理想的概念。我们证明一个具有极大理想M和重数e的数值半群是 GAS 当且仅当M – e是M – M 的一个近似正则理想. 这推广了 Barucci 关于几乎对称半群的结果和 Chau、Goto、Kumashiro 和 Matsuoka 关于 2-AGL 半群的定理。我们还研究了 GAS 属性从数值半群到它的胶合、数值复制和膨胀的转移。