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| Paper IPM / M / 17875 |
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| Abstract: | |
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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 C-approximations and right C-approximations of simple Î-modules, 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 Î-modules in C.
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