• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.278-282
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• 2014

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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.871-878
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• 2007

We define a numerical invariant $row_{CM}(A)$ over Cohen-Macaulay local ring A, which is related to rows of the presenting matrices of maximal Cohen-Macaulay modules without free summands. We show that $row(A)=row_{CM}(A)$ for a Cohen-Macaulay(not necessarily Gorenstein) local ring A.

• Journal of Integrative Natural Science
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• v.10 no.4
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• pp.240-244
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• 2017

We study the behavior of some invariants under completion. We also give a counterexample, which is the same as a counterexample to Ding's Conjecture, to Koh-Lee's Conjecture.