Bulletin of the
Korean Mathematical Society BKMS

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