环到其典范模的嵌入
On embeddings of rings into their canonical modules
- Thai Nguyen University of Education（越南太原教育大学）
- Osaka Institute of Technology（大阪工业大学）
- Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文研究Cohen-Macaulay局部环到典范模的嵌入，提出Ext消逝准则并刻画纤维积、数值半群环及图的Stanley-Reisner环中的直和项条件，等价于严格重数不等式。
中文摘要 AI 辅助
我们研究Cohen-Macaulay局部环到其典范模的嵌入，使得余核被一个正则序列商后，其商包含剩余域作为直和项。受几乎Gorenstein环的启发，我们证明了有限射影维数的Ext消逝准则，该准则蕴含G-正则性和广义Auslander-Reiten条件。我们刻画了一维纤维积和数值半群环的这一直和项条件。对于图的Stanley-Reisner环，我们以图的语言刻画了分次嵌入的相应条件，并证明其等价于一个严格重数不等式。
英文摘要
We study embeddings of Cohen--Macaulay local rings into their canonical modules such that the quotient of the cokernel by a regular sequence has the residue field as a direct summand. Motivated by almost Gorenstein rings, we prove an Ext-vanishing criterion for finite projective dimension, which implies G-regularity and the generalized Auslander--Reiten condition. We characterize this summand condition for one-dimensional fiber products and numerical semigroup rings. For Stanley--Reisner rings of graphs, we characterize the corresponding condition for graded embeddings in terms of the graph and show that it is equivalent to a strict multiplicity inequality.
