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Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness

Global Wildness and Tameness

This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)

(ii) [M'] - [M" e ker(£"(*) (difference computed in g(M)). (iii) M'e N = M" G. N.
Moreover, ker(£*(*N)) crg(M). PROOF. For A € genus(M), we note that (25.9.1)
can be rewritten as the equivalence: (26.2.1) [A] e ker(£"(*) = A B N = Me N For
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