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SUMMARY:Oana Veliche (Northeastern University)
DTSTART:20200921T161500Z
DTEND:20200921T171500Z
DTSTAMP:20260423T021706Z
UID:GASC/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GASC/1/">A c
 lassification of generic type 2 artinian rings</a>\nby Oana Veliche (North
 eastern University) as part of Geometry\, Algebra\, Singularities\, and Co
 mbinatorics\n\n\nAbstract\nThe commutative local rings are usually placed 
 in the following hierarchy\,  based on the character of their singularity:
  regular\, hypersurface\, complete intersection\, and Gorenstein. These cl
 asses would be enough to describe all the rings of codepth 0 and 1. Howeve
 r\, a new class is needed to describe all the rings of codepth 2. This is 
 the class of Golod rings\; an example of such a ring is the quotient of an
 y local ring by the square of the maximal ideal. Such a classification is 
 still possible for all  codepth 3 rings if one considers the multiplicativ
 e structure of the Tor-algebra of the ring. The Golod rings are exactly th
 e rings with trivial multiplication. \n\nIn a joint work with Lars W. Chri
 stensen we completely classify the Artinian compressed rings of type 2 of 
 codepth 3 that are obtained from two compressed Gorenstein rings (rings of
  type 1). We prove that the class of all generic Artinian rings of type 2 
 is exactly determined by only two easily computable numbers\, namely the s
 ocle degrees of the two Gorenstein rings.\n
LOCATION:https://researchseminars.org/talk/GASC/1/
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