Finitistic dimension and Igusa–Todorov algebras
نویسندگان
چکیده
منابع مشابه
On finitistic dimension of stratified algebras
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
متن کاملFinitistic Dimension through Infinite Projective Dimension
We show that an artin algebra Λ having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with vanishing radical cube. We also give an equivalence between the finiteness of fin.dim.Λ and the finiteness of a given class of Λ-modules of infinite projective dimension.
متن کاملFinitistic Dimensions of Monomial Algebras
Theorem. (Auslander-Buchsbaum-Serre, 1956; see [2] and [24].) Let V be an affine algebraic variety over an algebraically closed field with coordinate ring R. Then the global dimension of R is finite if and only if V is smooth. If this is the case, then gl dimR = dimV . (That the global dimension of R is bounded above by n means that n-fold iteration of the process of taking syzygies of R-module...
متن کاملComparison of Views on Finitistic Projective Dimension
The finitistic dimension conjecture says that the projective dimension of finitely generated modules over an Artin algebra is bounded when finite. The conjecture is known for algebras of representation dimension 3, for modules of Loevey length 2 and for stratifying systems with at most 2 indecomposable modules of infinite projective dimension (Huard, Lanzilotta, Mendoza [4]). We would like to i...
متن کاملAn Approach to the Finitistic Dimension Conjecture
Let R be a finite dimensional k-algebra over an algebraically closed field k and modR be the category of all finitely generated left R-modules. For a given full subcategory X of modR, we denote by pfdX the projective finitistic dimension of X . That is, pfdX := sup {pdX : X ∈ X and pdX < ∞}. It was conjectured by H. Bass in the 60’s that the projective finitistic dimension pfd (R) := pfd (modR)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2009
ISSN: 0001-8708
DOI: 10.1016/j.aim.2009.07.008