In his work on the Bass series of syzygy modules of modules over a commutative noetherian local ring R, Lescot introduces a numerical invariant, denoted σ (R), and asks whether it is finite for any R. He proves that this is so when R is Gorenstein or Golod. In the present work many new classes of rings R for which σ (R) is finite are identified. The new insight is that σ (R) is related to the natural map from the usual cohomology of the module to its stable cohomology, which permits the use of multiplicative structures to study the question of finiteness of σ (R).
Iyengar et al. (Thu,) studied this question.