Syzygy modules with semidualizing or G-projective summands |
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Institution: | Department of Mathematics, Faculty of Science, Okayama University, 1-1, Naka 3-chome, Tsushima, Okayama 700-8530, Japan |
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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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