Torsion functors of generalized local cohomology modules

Let R be a commutative Noetherian ring, 𝔞 an ideal of R, M a finite R–module with finite projective dimension, and X an arbitrary R–module. In this paper, for fixed integers s,t and an arbitrary R–module N, we study the membership of TorsR(N,H𝔞t(M,X)) in Serre subcategories of the category of R–modules. We present some upper bounds for the flat dimension and the Betti numbers of H𝔞t(M,X). We also give some results on cofiniteness, finiteness, vanishing, and Artinianness of generalized local cohomology modules.