Direct summands of syzygy modules of the residue class field

Details Direct summands of syzygy modules of the residue class field Direct summands of syzygy modules of the residue class field

2007-03-07

arxiv.org/abs/math/0703186v1

Mathematics

Commutative Algebra

18 pages, to appear in Nagoya Mathematical Journal

Scientific paper

Let R be a commutative Noetherian local ring. This paper deals with the
problem asking whether R is Gorenstein if the n-th syzygy of the residue field
of R has a nontrivial direct summand of finite G-dimension for some n. It is
proved that if n is at most two then it is true, and moreover, the structure of
the ring R is determined essentially uniquely.

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