Presenting matrices of maximal Cohen-Macaulay modules
Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 871-878
Published online December 1, 2007
Kisuk Lee
Sookmyung Women's University
Abstract : We define a numerical invariant $\mathrm{row}_{CM}(A)$ over Cohen-Mac\-aulay local ring $A$, which is related to rows of the presenting matrices of maximal Cohen-Macaulay modules without free summands. We show that $\mathrm{row}(A)= \mathrm{row}_{CM}(A)$ for a Cohen-Macaulay (not necessarily Gorenstein) local ring $A$.
Keywords : column and row invariants, maximal Cohen-Macaulay modules, syzygy modules, Cohen-Macaulay ring
MSC numbers : 13H10, 13C14, 13D02
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