On the finitistic dimension conjecture II: Related to finite global dimension
โ Scribed by Changchang Xi
- Book ID
- 108051433
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 327 KB
- Volume
- 201
- Category
- Article
- ISSN
- 0001-8708
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## Abstract We explore the interlacing between model category structures attained to classes of modules of finite \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {X}$\end{document}โdimension, for certain classes of modules \documentclass{article}\usepackage{ams
It is shown that, given any left artinian ring \(A\) which has vanishing radical cube and \(n\) isomorphism classes of simple left modules, the global dimension of \(A\) is either infinite or bounded above by \(n^{2}-n\), and the left finitistic dimension of \(A\) is always less than or equal to \(n
In this note we prove that for a left artinian ring of infinite global dimension there exists an indecomposable left module with both infinite projective dimension and infinite injective dimension. ๏ฃฉ 2002 Elsevier Science (USA) The purpose of this note is to prove the following theorem motivated by