具有半对偶或G-投射和项的合模
Syzygy modules with semidualizing or G-projective summands
摘要：
设R是具有剩余域k的交换Noether局部环.本文主要研究k的合冲模的直和项。我们证明了R是正则的当且仅当k的某个合模有一个半对偶和项。然后考虑R是Gorenstein的充要条件是k的某个合冲模有G-投射和项。
英文摘要：
Let R be a commutative Noetherian local ring with residue class field k. In this paper, we mainly investigate direct summands of the syzygy modules of k. We prove that R is regular if and only if some syzygy module of k has a semidualizing summand. After that, we consider whether R is Gorenstein if and only if some syzygy module of k has a G-projective summand.
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。
