We introduce the concept of modified vertical Weil functors on the category \mathcal{F}\mathcal{M}_m of fibred manifolds with m-dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on \mathcal{F}\mathcal{M}_m in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil functors T^{a} corresponding to Weil algebras A by the so called modified Weil functors T^{a} corresponding to Weil algebra bundle functors A on the category \mathcal{F}\mathcal{M}_m of m-dimensional manifolds and their embeddings., Włodzimierz M. Mikulski., and Obsahuje seznam literatury
We study the relations between finitistic dimensions and restricted injective dimensions. Let R be a ring and T a left R-module with A = EndRT. If RT is selforthogonal, then we show that rid \left ( T_{A} \right )\leqslant findim(A_{A})\leqslant findim \left ( _{R}T \right )+rid\left ( T_{A} \right ). Moreover, if R is a left noetherian ring and T is a finitely generated left R-module with finite injective dimension, then rid \left ( T_{A} \right )\leqslant findim(A_{A})\leqslant fin.inj.dim \left ( _{R}R \right )+rid\left ( T_{A} \right ). Also we show by an example that the restricted injective dimensions of a module may be strictly smaller than the Gorenstein injective dimension., Dejun Wu., and Obsahuje seznam literatury