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Syzygy modules with semidualizing or G-projective summands

Ryo Takahashi
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Abstract

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.

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Ryo Takahashi. 2005-01-21. Syzygy modules with semidualizing or G-projective summands. https://arxiv.org/abs/math/0501342

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