Abstract
In this paper we give necessary and sufficient conditions for the linkage maps Φr (r = 1, 2) to be surjective onto the set of isomorphism classes of Cohen-Macaulay modules. More precisely, for a Gorenstein complete local ring R, we prove that Φ1 is surjective iff R is an integral domain, and that Φ2 is surjective iff R is a unique factorization domain.
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References
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Y. Yoshino and S. Isogawa, Linkage of Cohen-Macaulay modules over a Gorenstein ring, J. Pure and Applied Algebra 149 (2000), 305–318.
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Yoshino, Y. (2001). Surjectivity of Linkage Maps. In: Birkenmeier, G.F., Park, J.K., Park, Y.S. (eds) International Symposium on Ring Theory. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0181-6_30
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DOI: https://doi.org/10.1007/978-1-4612-0181-6_30
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6650-1
Online ISBN: 978-1-4612-0181-6
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