Abstract
IF E is any additive category, the Grothendieck group Kc%?) is defined to be the group with one generator [A] for each object A of V and relations [A] = [A’] + [A”] whenever there is an exact sequence 0 + A’ + A -+ A” -+ 0 in %’ [6], [23]. If R is a commutative ring and rr is a finite group, I will denote by G(Rrr) the Grothendieck group of the category of finitely generated: Rn-modules [23]. The main purpose of this paper is to obtain information about the structure of G(Rn) when R is a Dedekind ring.
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