On the Number of Totally Reflexive Modules

Specialeforsvar ved Anders Friis Frand-Madsen

Titel: On the Number of Totally  Reflexive Modules

Abstract: The object of study in this thesis is the subcategory of totally reflexive modules G (R) of the category of finitely generated modules over a commutative local Noetherian ring R. To understand G (R), it is, in some sense, enough to understand all the indecomposable modules, as these are the building blocks of the rest of the modules in G (R). Therefore, an obvious question to ask is how many of such indecomposable modules there are. The main result in this thesis provides a quite concrete answer to this question: If there are only finitely many indecomposable totally reflexive modules, up to isomorphism, then we are in one of two situations: (1) the ring we are working over is Gorenstein, or (2) there is in fact only one indecomposable module, namely the one-dimensional free module over R.

Vejleder: Henrik G. Holm
Censor:   Niels Lauritzen, Aarhus universitet