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Koszul Modules and Gorenstein Algebras

✍ Scribed by M. Grassi

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 306 KB
Volume: 180
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0102

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✦ Synopsis

I first define Koszul modules, which are a generalization to arbitrary rank of complete intersections. After a study of some of their properties, it is proved that Gorenstein algebras of codimension one or two over a local or graded CM ring are Koszul modules, thus generalizing a well known statement for rank one modules. The general techniques used to describe Koszul modules are then used to obtain a structure theorem for Gorenstein algebras in codimension one and two, over a local or graded CM ring.

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