THE TWENTIETH COLLOQUIUMFEST

Speaker: Hagen Knaf 

Title: On the Cohen-Macaulay-property for non-noetherian rings

Abstract: 
While there are straightforward non-noetherian generalisations
of important classes of noetherian rings like principal ideal domains,
Dedekind domains, regular rings and normal noetherian rings, this is
not the case for the class of Cohen-Macaulay rings.

In the past at least two attempts to generalise the Cohen-Macaulay-property
have been published: one by Michinori Sakaguchi in 1980 and a second one
by Tracy Hamilton and Thomas Marley in 2006. Both attempts did not lead to
a completely satisfying definition. For example in both cases the Cohen-Macaulay
property is not stable under taking factor rings with respect to ideals
generated by regular sequences.

In the talk Sakaguchi's approach is discussed taking into account results
that were obtained only after he published his work.