The Grothendieck Group and the Extensional Structure of Noetherian Module Categories

@inproceedings{Brookfield2003TheGG,
title={The Grothendieck Group and the Extensional Structure of Noetherian Module Categories},
author={Gary Brookfield},
year={2003}
}

Gary Brookfield

Published 2003

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 commutative monoids. In this paper the relationship between these two universal objects is studied leading to a new and more detailed description of the former. There is a natural decomposition G0(R… CONTINUE READING