Computation of numerical invariants $col(-), row(-)$ for a ring $k[t^e, t^{e + 1}, t^{(e - 1) e - 1}]$

Kisuk Lee

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J. Korean Math. Soc. 2000; 37(4): 521-530

Printed July 1, 2000

Computation of numerical invariants $col(-), row(-)$ for a ring $k[t^e, t^{e + 1}, t^{(e - 1) e - 1}]$

Kisuk Lee

Sookmyung Women's University

Abstract

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Abstract

\baselineskip 15pt We find the values of numerical invariants $col(R)$ and $row(R)$ for $R$ = $k[\![t^e,t^{e+1},t^{(e-1)e-1}]\!]$, where $k$ is a field and $e \ge 4$. We also show that $col(R)=crs(R)$ and $row(R)=drs(R)$, but they are strictly less than the reduction number of $R$ plus $1$.

Keywords: invariants, reduction number, Loewy length, Cohen-Macaulay ring

MSC numbers: 13H10, 13C14, 13D02