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|Paper IPM / M / 16945||
Let A be an artin algebra and M be an n-cluster tilting subcategory of
modA. We show that M has an additive generator if and only if the n-almost split sequences form a basis for the relations for the Grothendieck group of M if and only if every effaceable functor from M to the category of abelian groups Ab has finite length. As a consequence we show that if modA has n-cluster tilting subcategory of finite type then the n-almost split sequences
form a basis for the relations for the Grothendieck group of A.
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