Let AA be an abelian category having enough projective objects and enough injective
objects. We prove that if AA admits an additive generating object, then the extension …

We prove that for a Frobenius extension, a module over the extension ring is Gorenstein
projective if and only if its underlying module over the base ring is Gorenstein projective. For …

For any exact category A with splitting idempotents, a maximal exact category T (A)
containing A as a biresolving subcategory, is constructed. Important types of exact …

In this paper, we introduce the notion of weak excellent extensions of rings as a
generalization of that of excellent extensions of rings. Let Γ be a weak excellent extension of …

In 2005, the second author and Todorov introduced an upper bound on the finitistic
dimension of an Artin algebra, now known as the ϕ ϕ-dimension. The ϕ ϕ-dimension …

We consider a class of extensions of both abstract and pseudocompact algebras, which we
refer to as" strongly proj-bounded extensions". We prove that the finiteness of the left global …

Finitistic dimension through infinite projective dimension Page 1 Bull. London Math. Soc. 41
(2009) 367–376 Cо2009 London Mathematical Society doi:10.1112/blms/bdp010 Finitistic …

The famous finitistic dimension conjecture says that every finite-dimensional 𝕂-algebra over
a field 𝕂 should have finite finitistic dimension. This conjecture is equivalent to the following …

In this paper, we develop new ideas regarding the finitistic dimension conjecture, or the
findim conjecture for short. Specifically, we improve upon the delooping level by introducing …

ON THE REPRESENTATION DIMENSION OF TILTED AND LAURA ALGEBRAS The chief
objective of the representation theory of artin algebras Page 1 ON THE REPRESENTATION …