Ki-Suk Lee
Abstract
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We define a numerical invariant $row^*_j(A)$ over Cohen-Macaulay local ring A, which is related to the presenting matrices of the j-th syzygy module (with or without free summands). We show that $row_d(A)$ = $row_{CM}(A)$ and $row^*_d(A)$ = $row^*_{CM}(A)$ for a Cohen-Macaulay local ring A of dimension d.
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We define a numerical invariant $row^*_j(A)$ over Cohen-Macaulay local ring A, which is related to the presenting matrices of the j-th syzygy module (with or without free summands). We show that $row_d(A)$ = $row_{CM}(A)$ and $row^*_d(A)$ = $row^*_{CM}(A)$ for a Cohen-Macaulay local ring A of dimension d.
Key concepts: Hilbert's syzygy theorem, Local ring, Mathematics, Invariant (physics), Pure mathematics, Dimension (graph theory), Combinatorics, Ring (chemistry)