The Grothendieck Group and the Extensional Structure of Noetherian Module Categories

  title={The Grothendieck Group and the Extensional Structure of Noetherian Module Categories},
  author={Gary Brookfield},
  • 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

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