It is proved that an element r in the center of a coherent ring annihilates Ext n (M, N ), for some positive integer n and all finitely presented -modules M and N , if and only if the bounded derived category of is an extension of the subcategory consisting of complexes annihilated by r and those obtained as n-fold extensions of . This has applications to finiteness of dimension of derived categories.
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Iyengar et al. (2014) studied this question.
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