2,488 research outputs found
Remarks on modules approximated by G-projective modules
Let be a commutative Noetherian Henselian local ring. Denote by
the category of finitely generated -modules, and by
the full subcategory of consisting of all
G-projective -modules. In this paper, we consider when a given -module
has a right -approximation. For this, we study the full
subcategory of consisting of all
-modules that admit right -approximations. We investigate the
structure of by observing , and , where
denotes the full subcategory of consisting of all -modules
that admit left -approximations. On the other hand, we also
characterize in terms of Tate cohomologies. We give
several sufficient conditions for to be contravariantly finite
in .Comment: 28 pages, to appear in J. Algebr
Syzygy modules with semidualizing or G-projective summands
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.Comment: 13 pages, to appear in Journal of Algebr
Reconstruction from Koszul homology and applications to module and derived categories
Let R be a commutative noetherian ring. Let M be a finitely generated
R-module. In this paper, we reconstruct M from its Koszul homology with respect
to a suitable sequence of elements of R by taking direct summands, syzygies and
extensions, and count the number of those operations. Using this result, we
consider generation and classification of certain subcategories of the category
of finitely generated R-modules, its bounded derived category and the
singularity category of R.Comment: 14 pages, final version, to appear in Pacific J. Mat
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