On non Artinian cofinite generalized local cohomology modules
Let \(R\) be a commutative Noetherian ring and \(I\subseteq J\) be ideals of \(R\). Let \(M\) and \(N\) be finitely generated \(R\)-modules such that projective dimension of \(M\) is finite. Let \(q_I(M, N) = \sup\{i\in\mathbb{N}_0 : H^i_ I(M, N)\) is not Artinian I-cofinite\(\}\), where \(H^i_I(M,N)\) is the generalized local cohomology module. In the paper under review, the author proves that \(q_J(M, N)\le q_I(M, N)+ \mathrm{cd}_J(M, N/IN)\), where \(\mathrm{cd}_J(M,N/IN)\) is the cohomological dimension of \(m\) and \(N/IN\) with respect to ideal \(J\).
scientific article; zbMATH DE number 7599156
scientific article