Advanced Studies: Euro-Tbilisi Mathematical Journal

On non Artinian cofinite generalized local cohomology modules

F. Vahdanipour

Let R be a commutative Noetherian ring and I ⊆ J be ideals of R. Let M and N be finitely generated R-modules such that pd_R(M) < ∞. In this paper, we study the supremum of non Artinian I-cofinite modules Hⁱ_I(M,N) over a commutative Noetherian ring where i ≤ 1 and give a bound for q_J(M,N) by using q_I(M,N). We show that q_J(M,N) ≤ q_I(M,N) + cd_J(M,N/IN).


Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 15(3) (2022), pp. 45-51