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Finitistic Dimension and Restricted Flat Dimension by Jiaqun Wei is a Mathematics article available to read on EtoBox.
What is Finitistic Dimension and Restricted Flat Dimension about?
We investigate the relations between finitistic dimensions and restricted flat dimensions (introduced by Foxby [L.W. Christensen, H.-B. Foxby, A. Frankild, Restricted homological dimensions and Cohen-Macaulayness, J. Algebra 251 (1) (2002) 479-502]). In particular, we show the following result. (1) If T is a selforthogonal left module over a left noetherian ring R with the endomorphism ring A, then rfd(T A ) R are Artin algebras with the same identity such that, for each 0 i m -1, rad A i is a right ideal in A i+1 and rfd(A i+1 A i ) < ∞ (e.g., A i+1 A i is of finite projective dimension, or finite Gorenstein projective dimension, or finite Tor-bound dimension), then fdim( R R) < ∞ implies fdim( A A) < ∞. As applications, we disprove Foxby's conjecture [H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004) 167-193] on restricted flat dimensions by providing a counterexample and give a partial answer to a question posed by Mazorchuk [V. Mazorchuk, On finitistic dimension of stratified algebras, arXiv:math.RT/0603179, 6.4].
Who reads Finitistic Dimension and Restricted Flat Dimension?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Jiaqun Wei
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0021-8693)
- Published
- 2008
- Language
- EN
- Field
- Mathematics (Physical Sciences)