@article {
author = {Bagherian, Roghayeh and Hosseini, Esmaeil},
title = {Big Finitistic Dimensions for Categories of Quiver Representations},
journal = {Mathematics Interdisciplinary Research},
volume = {6},
number = {2},
pages = {139-149},
year = {2021},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2021.240439.1273},
abstract = {Assume that A is a Grothendieck category and R is the category of all A-representations of a given quiver Q. If Q is left rooted and A has a projective generator, we prove that the big finitistic flat (resp. projective) dimension FFD(A) (resp. FPD(A)) of A is finite if and only if the big finitistic flat (resp. projective) dimension of R is finite. When A is the Grothendieck category of left modules over a unitary ring R, we prove that if FPD(R) < +∞ then any representation of Q of finite flat dimension has finite projective dimension. Moreover, if R is n-perfect then we show that FFD(R) < +∞ if and only if FPD(R) < +∞. },
keywords = {Quiver,representation of quiver,Grothendieck category,finitistic dimension},
url = {https://mir.kashanu.ac.ir/article_111485.html},
eprint = {https://mir.kashanu.ac.ir/article_111485_e92e83f51ff8b7f5bd417fe9bbecf04e.pdf}
}