Primary decomposition of modules: a computational differential approach
Primary decomposition of modules: a computational differential approach
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DOI：
10.1016/j.jpaa.2022.107080
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发表时间：
2021-04
影响因子：
0.8
通讯作者：
Justin Chen;Yairon Cid‐Ruiz
中科院分区：
文献类型：
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作者：
Justin Chen;Yairon Cid‐Ruiz
我们从微分和计算的角度研究了主子模和初等分解。我们的主要理论贡献是给出了多项式环上任意非线性生成模的准素子模的一般结构理论和表示定理。我们刻画的微分算子和准时报价计划的主子模。此外，我们介绍并实现了一个算法，计算一个模块的最小微分主分解。
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary finitely generated module over a polynomial ring. We characterize primary submodules in terms of differential operators and punctual Quot schemes. Moreover, we introduce and implement an algorithm that computes a minimal differential primary decomposition for a module.