کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587622 1334151 2008 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An approach to the finitistic dimension conjecture
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
An approach to the finitistic dimension conjecture
چکیده انگلیسی

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, .It was conjectured by H. Bass in the 60's that the projective finitistic dimension pfd(R):=pfd(modR) has to be finite. Since then, much work has been done toward the proof of this conjecture. Recently, K. Igusa and G. Todorov defined in [K. Igusa, G. Todorov, On the finitistic global dimension conjecture for artin algebras, in: Representations of Algebras and Related Topics, in: Fields Inst. Commun., vol. 45, Amer. Math. Soc., Providence, RI, 2005, pp. 201–204] a function , which turned out to be useful to prove that pfd(R) is finite for some classes of algebras. In order to have a different approach to the finitistic dimension conjecture, we propose to consider a class of full subcategories of modR instead of a class of algebras. That is, we suggest to take the class of categories F(θ), of θ-filtered R-modules, for all stratifying systems (θ,⩽) in modR. We prove that the Finitistic Dimension Conjecture holds for the categories of filtered modules for stratifying systems with one or two (and some cases of three) modules of infinite projective dimension.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 319, Issue 9, 1 May 2008, Pages 3918-3934