幺半群同余的中初等分解
On mesoprimary decomposition of monoid congruences
摘要：
本文证明了Kahle和Miller提出的关于幺半群同余的介初等分解的两个主要结果。首先，我们确定哪些相关联的素同余出现在每一个mesoprimary分解，从而完成的mesoprimary分解理论的幺半群同余作为一个更忠实的模拟准素分解。其次，我们回答了一个问题所提出的Kahle和米勒的特点，有限偏序集出现的一套相关素同余的幺半群同余。
英文摘要：
We prove two main results concerning mesoprimary decomposition of monoid congruences, as introduced by Kahle and Miller. First, we identify which associated prime congruences appear in every mesoprimary decomposition, thereby completing the theory of mesoprimary decomposition of monoid congruences as a more faithful analog of primary decomposition. Second, we answer a question posed by Kahle and Miller by characterizing which finite posets arise as the set of associated prime congruences of monoid congruences.
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。
