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BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 23, Number 1, July 1990
GORENSTEIN LOCAL HOMOMORPHISMS
LUCHEZAR L. AVRAMOV AND HANS­BJØRN FOXBY
Introduction
A Noetherian local ring is the algebraic version of a ring of germs
of functions defined in neighborhoods of some point of an algebraic
(or analytic) variety. Accordingly, local rings are naturally classi­
fied by the complexity of the singularity they describe, with the
simplest class consisting of the regular rings, which correspond to
nonsingular points. On the singular side a natural boundary is
provided by the Cohen­Macaulay rings: beyond them pathological
(that is, geometrically unpredictable) behavior becomes a common
phenomenon.
During the last three decades much of the work in commutative
algebra has concentrated on rings whose singularities interpolate
between these two extremes. One of the most important develop­
ments early in that period was the discovery of the intermediate
class of Gorenstein rings by Bass and Grothendieck. These authors

  

Source: Avramov, Luchezar L.- Department of Mathematics, University of Nebraska-Lincoln

 

Collections: Mathematics