交换么半群同余与二项式理想的分解
Decompositions of commutative monoid congruences and binomial ideals
摘要：
交换幺半群同余的准素分解对交换环中的准素分解的某些特征不敏感。这些特征被更精细的同余解的介元分解理论所捕捉，这里介绍的是完整的见证人和相关的素对象。中初等分解的组合理论提升到幺半群代数中的任意二项理想。所得的二项式中初等分解是一种新的二项式理想的交分解，具有计算效率和独立于基域假设。二项式准素分解很容易从中间主分解中恢复出来。
英文摘要：
Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences, introduced here complete with witnesses and associated prime objects. The combinatorial theory of mesoprimary decomposition lifts to arbitrary binomial ideals in monoid algebras. The resulting binomial mesoprimary decomposition is a new type of intersection decomposition for binomial ideals that enjoys computational efficiency and independence from ground field hypotheses. Binomial primary decompositions are easily recovered from mesoprimary decomposition.
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。
