… Thus, E(M) is an injective module which we regard as containing M, and Mis essential in
£(M… the left finitistic dimensions of P as follows: 1 GP (P) = sup {P^r (,4 )| ,4 is a left P-module}. …

… 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 …

… 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. …

… Let 3 be the set of all paths in Z; we regard each vertex as a path of length 0 with t(ui) = ~$0~)
= ui, so Z, Eb . The path algebra kT of Z over k is the k-vector space with basis the set B, …

In this note we introduce the syzygy quiver R in order to improve the bound of the finitistic
global dimension of a monomial algebra h by following the lines of the proof of K. Igusa and D. …

… 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: …

… dimensions with respect to proper standard and proper costandard modules with the finitistic
dimension of … It also happens that the finitistic dimension of a properly stratified algebra is …

… dimension, and the algebraic K-theory and G-theory (see [1,2,4,6–8]). In this short note, we
point out that the finiteness of the finitistic dimension … Let A[M] and B[N] be the respective one-…

… that the little finitistic dimension can be strictly larger than the cyclic finitistic dimension and,
in fact, need not be attained … Call a submodule U of a left A-module M saturated (with respect …

… the finitistic projective dimension and the finitistic flat dimension of unitary rings, and in Sect.
3, we study the finitistic flat dimensions … objects and their finitistic projective dimension is not …