… More precisely, we define the M -cohomological dimension of M relative to I, denoted by M -
cd ( I , … For any R-module N, we use the notation E R ( N ) for the injective envelope of the R-…

… for injective dimension. As an application we obtain some results on the injective dimension
of local cohomology modules. … a Cohen–Macaulay R-module of finite projective dimension. …

… discuss the homological dimensions of R in terms of P1-injective modules. In … dimension
and the global dimension of a ring R: wgl-dim(R) = sup{fdR(M) : M is a P1-injective left R-module…

… p and M be an F-finite module. In this paper, we study the injective dimension of M. We prove
that … result for a class of holonomic D-modules which contains local cohomology modules. …

… to build injective resolutions. From there, we establish a lower bound for the associated global
dimension. … algebra for operator modules over a C*-algebra. We provide a proof that the …

… of Gorenstein injective dimension of all R-modules in D is finite… to define a notion of relative
cohomology group Ext GI n ( C , D … dimension and D a complex with finite Gorenstein injective …

… In the next section we will recall the notions of injective dimension and local cohomology
over derived commutative rings. In this context, local cohomology is taken with respect to ideals …

… show that the local cohomology functor RΓ aassociated with a does not increase injective
dimension. Dually, the derived a-adic completion functor LΛ a does not increase at dimension. …

… dimensions and the injective dimensions for DG-modules introduced by Yekutieli. We explain
the details by focusing on the projective dimension and … H0 of the 0-th cohomology algebra …

… M over a power series ring R = k [ x 1 , … , x n ] , the dimension of the top de Rham cohomology
module H D R n ( M ) is equal to the largest number of copies of the injective envelope E …