Decompositions of commutative monoid congruences and binomial ideals
Decompositions of commutative monoid congruences and binomial ideals
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交换幺半群同余和二项式理想的分解
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Ezra Miller
中科院分区：
文献类型：
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作者：
Thomas Kahle;Ezra Miller
交换幺半群同余的准素分解对交换环中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。由此得到的二项式中初等分解是一种新的二项式理想的交集分解，具有计算效率高和不依赖于基场假设的优点。二项式初等分解很容易从中初等分解恢复。
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.