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Paper IPM / M / 17875  


Abstract:  
Let Î be an artin algebra and C be a functorially finite subcategory of modÎwhich contains Îor DÎ. We use the concept of the infinite radical of C and show that Chas an additive generator if and only if radâCvanishes. In this case, we describe the morphisms in powers of the radical of C in terms of its irreducible morphisms. Moreover, under a mild assumption, we prove that C is of finite representation type if and only if any family of monomorphisms (epimorphisms) between indecomposable objects in Cis noetherian (conoetherian). Also, by using injective envelopes, projective covers, left Capproximations and right Capproximations of simple Îmodules, we give other criteria to describe whether C is of finite representation type. In addition, we give a nilpotency index of the radical of C which is independent from the maximal length of indecomposable Îmodules in C.
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