This research reveals interactions between the homological dimensions of Ext modules and finitely generated modules, suggesting key implications.
Let R be a commutative Noetherian local ring and let M and N be nonzero finitely generated R-modules. In this paper, we investigate how the finiteness of the homological dimension of Ext modules between M and N affects that of M and N. One of our main result states that if ExtⁱR(M,N) has finite projective dimension for any 0≤ i≤ RfdR M, where RfdR M is the (large) restricted flat dimension of M, then M has finite projective or injective dimension if and only if N does.
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Kaito Kimura (2025) studied this question.
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