… Finitistic Dimension Conjecture is one of the main open problems in the representation theory
of algebras. It … Finally, we prove that the finitistic dimension is bounded by the homological …

… with the endomorphism ring of a projective module over a hereditary or semihereditary
ring. More specifically we consider the question of when such an endomorphism ring is …

… It is worth noting that in the literature “monomial algebra” sometimes means a path algebra
… classes offinite dimensional algebras because being a monomial algebra is not an algebra …

… as hyperhomological algebra—and their applications in commutative algebra. We want to
make the case that these methods, compared to those of classic homological algebra, provide …

… finitistic dimension of some given algebra. The reader could look in [32], [49], and references
therein, for the development related with the finitistic dimension … local endomorphism rings. …

… algebras are gendo-symmetric algebras, which means endomorphism algebras of generators
of symmetric algebras, … characterization of dominant dimension for the algebras in terms of …

… result that characterizes the finite dimensional vector spaces (a … ) endomorphism of M is an
automorphism of M, and we say that M satisfies the property (F), if for each endomorphism f of …

… the algebra Λ. We show that the left finitistic and ϕ-dimensions are equal to the right finitistic
… As we will explain in 2.7, we did not take the opposite of the endomorphism algebra wittingly…

… Then we consider briefly the question of when the endomorphism ring of a finitely generated
… Zelinsky [15] who proved that the endomorphism ring of a PF module over a quasi-…

… the context of finitely generated modules over artin algebras, as dual of the concept of tilting
… noetherian rings which are noetherian over their endomorphism ring. Next, the notion has …