The Grothendieck Group and the Extensional Structure of Module Categories
by
Gary Brookfield
University of Wisconsin, Madison

For a left Noetherian ring R, the Gothendieck group G₀(R) is universal for maps which respect short exact sequences from the category of left Noetherian R-modules to Abelian groups. There is a less well known monoid M(R-Noeth) which has the analogous universal property with respect to maps into monoids. In this talk I will discuss the interesting relationship between these two universal objects. In particular, I will explain how G₀(R) embeds in M(R-Noeth) and, more generally, how the Gothendieck group of every factor ring of R embeds in M(R-Noeth).

Date received: February 9, 1999