Abstract
Let [Formula: see text] be a Morita ring which is an Artin algebra and has zero bimodule homomorphisms. Assume that [Formula: see text] and [Formula: see text] are projective modules. For any positive integer [Formula: see text], it is proved that [Formula: see text] is [Formula: see text]-Igusa–Todorov (respectively, [Formula: see text]-syzygy-finite) if and only if [Formula: see text] and [Formula: see text] are [Formula: see text]-Igusa–Todorov (respectively, [Formula: see text]-syzygy-finite).
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