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Paper IPM / M / 14969  


Abstract:  
Let (R, \mathfrakm, k) be a commutative Noetherian local ring.
We study the suitable chains of semidualizing Rmodules.
We prove that when R is Artinian, the existence of
a suitable chain of semidualizing modules of length n=max { i\geqslant 0  \mathfrakm^{i} ≠ 0 }
implies that the the Poincar\acutee series of k and the Bass series of R have very specific forms.
Also, in this case we show that the Bass numbers of R are strictly increasing. This gives an insight into
the question of Huneke about the Bass numbers of R.
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