… We may regard X as an A-module via the canonical map. Thus the map A ⊗B X → AX is
a split map. Now we apply A ⊗A − to this split map and get a split homomorphism …

… M ) < ∞ } and the related finitistic Gorenstein projective dimension of the base ring R as
follows… R-module C, we define the finitistic projective dimension of R with respect to C as follows: …

… of (finitistic) global dimensions; we describe each by specifying the type of dimension and
the modules … Thus, E(M) is an injective module which we regard as containing M, and M is …

… A) the finitistic dimension of A, and by proj.dim(X) the projective dimension of a module X
in A… Let A[M] and B[N] be the respective one-point extensions. If A and B are derived-equivalent, …

… modules, and we study the notion of filtration dimensions with respect to all these families.
The notions of filtration dimensions with respect to proper standard and proper costandard …

… -cotilting modules and finitistic n-self-cotilting modules. From … a finitistic (n + 1)-self-cotilting
module which is not a finitistic n… generated projective modules, and it is closed with respect to …

… Call a submodule U of a left A-module M saturated (with respect … Alternately, we observe
that the nonzero projective module M, and afortiori the module j(t), contains a cyclic submodule …

… dimensions of the finitely generated A-modules is the finitistic global dimension of A and the
finitistic … The generating set Z can be choscn to be minimal with respect to the ordering of the …

… Our aim is to obtain an upper bound on the finitistic dimension of S which applies when pd(…
( , R) we regard R as a left S-module to obtain a bound on the right finitistic dimension of R. …

… modules of finite Gorenstein projective dimension), and its relation to validity of finitistic
dimension … fin implies validity of the second finitistic dimension conjecture over left artinian rings. …