Syzygy modules with semidualizing or G-projective summands

Details Syzygy modules with semidualizing or G-projective summands Syzygy modules with semidualizing or G-projective summands

2005-01-21

arxiv.org/abs/math/0501342v1

Mathematics

Commutative Algebra

13 pages, to appear in Journal of Algebra

Scientific paper

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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