Syzygies of modules with positive codimension

AbstractA higher syzygy of a module with positive codimension is a maximal Cohen–Macaulay module that plays an important role in Cohen–Macaulay approximation over Gorenstein rings. We show that every maximal Cohen–Macaulay module is a higher syzygy of some positive codimensional module if and only if the ring is an integral domain. Also we discuss the hierarchy of rings with respect to Cohen–Macaulay approximation by codimensions of modules

Triangulated subcategories of extensions, stable t-structures, and triangles of recollements

In a triangulated category T with a pair of triangulated subcategories X and Y, one may consider the subcategory of extensions X*Y. We give conditions for X*Y to be triangulated and use them to provide tools for constructing stable t-structures. In particular, we show how to construct so-called triangles of recollements, that is, triples of stable t-structures of the form (X,Y), (Y,Z), (Z,X). We easily recover some triangles of recollements known from the literature.Comment: 12 pages. This is the final accepted version which will appear in the Journal of Pure and Applied Algebr