数值半群理想类单体的同构问题

Pub Date : 2024-04-16 DOI:10.1007/s00233-024-10429-7

P. A. García-Sánchez

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引用次数: 0

摘要

作为应用，我们证明了两个不同的数字半群不可能有最小值为零的理想的同构正集（关于集合包含）。我们还证明，给定两个数字半群 S 和 T，如果它们的理想类单体同构，那么 S 一定等于 T。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The isomorphism problem for ideal class monoids of numerical semigroups

From any poset isomorphic to the poset of gaps of a numerical semigroup S with the order induced by S, one can recover S. As an application, we prove that two different numerical semigroups cannot have isomorphic posets (with respect to set inclusion) of ideals whose minimum is zero. We also show that given two numerical semigroups S and T, if their ideal class monoids are isomorphic, then S must be equal to T.

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