$\mathbb N^n$的良子半群
Good subsemigroups of $\mathbb N^n$
摘要：
不可约奇异代数曲线的值半群及其分式理想是$\mathbb Z^n$的子幺半群，它们在下确界下是闭的，有一个导体，并且它们的元素满足一个特殊的相容性质.满足这三个条件的$\mathbb N^n$的幺半群在文献中被称为好半群，并且有不能实现为代数曲线的值半群的好半群的例子。在本文中，我们考虑好半群独立于他们的代数对应，在一个纯粹的组合设置。定义了生成元的好系统的概念，证明了极小好系统是唯一的。此外，我们给出了当$n=2$时计算好子半群的标准理想和Arf闭包的构造性方法。
英文摘要：
Value semigroups of non irreducible singular algebraic curves and their fractional ideals are submonoids of $\mathbb Z^n$ that are closed under infimums, have a conductor and fulfill a special compatibility property on their elements. Monoids of $\mathbb N^n$ fulfilling these three conditions are known in the literature as good semigroups and there are examples of good semigroups that are not realizable as the value semigroup of an algebraic curve. In this paper we consider good semigroups independently from their algebraic counterpart, in a purely combinatoric setting. We define the concept of good system of generators, and we show that minimal good systems of generators are unique. Moreover, we give a constructive way to compute the canonical ideal and the Arf closure of a good subsemigroup when $n=2$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
