Abstract
Let [Formula: see text] be a commutative Noetherian local ring. We study the suitable chains of semidualizing [Formula: see text]-modules. We prove that when [Formula: see text] is Artinian, the existence of a suitable chain of semidualizing modules of length [Formula: see text] implies that the Poincar[Formula: see text] series of [Formula: see text] and the Bass series of [Formula: see text] have very specific forms. Also, in this case, we show that the Bass numbers of [Formula: see text] are strictly increasing. This gives an insight into the question of Huneke about the Bass numbers of [Formula: see text].
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