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Modules with linear resolution over a polynomial ring in two variables

Published online by Cambridge University Press:  22 January 2016

Yuji Yoshino
Yuji Yoshino*
Affiliation:
Department of Mathematics Nagoya University, Chikusa-ku, Nagoya 464, Japan
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Let k be a field and let S be a polynomial ring k[x1, x2,…, xn] over k in n variables. An S-module M is called a module with linear resolution if M has a free resolution;

where, after taking suitable bases of free modules, all fi’s are matrices consisting of linear forms of S. The reader should be referred to Eisenbud- Goto [2, Sections 0 and 1] for elementary facts concerning modules with linear resolution.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 113 , March 1989 , pp. 89 - 98
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

[1] Dieudonné, Jean, Sur la réduction canonique des couples de matrices, Bull. Soc. Math. Fr., 74 (1946), 130–146.Google Scholar
[2] Eisenbud, David and Goto, Shiro, Linear free resolution and minimal multiplicity, Journal of Algebra, 88 (1984), 89–133.Google Scholar
[3] Greither, Cornelius, Die unzerlegbaren Moduln über k[x, y]/(x2, y2), Algebra-Berichte, Seminar F. Kasch, B. Pareigis, Nr. 39, Univ. München, 1979.Google Scholar