Tilting theory and the finitistic dimension conjectures期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Tilting theory and the finitistic dimension conjectures

Authors:	Lidia Angeleri-Hü gel Jan Trlifaj

Institution:	Mathematisches Institut der Universität, Theresienstrasse 39, D-80333 München, Germany ; Katedra algebry MFF UK, Sokolovsk\a'a 83, 186 75 Prague 8, Czech Republic

Abstract:	Let be a right noetherian ring and let $\mathcal{P}^{<\infty}$ be the class of all finitely presented modules of finite projective dimension. We prove that findim $R = n < \infty$ iff there is an (infinitely generated) tilting module such that pd and $T ^\perp = (\mathcal P^{<\infty})^\perp$ . If is an artin algebra, then can be taken to be finitely generated iff $\mathcal P^{<\infty}$ is contravariantly finite. We also obtain a sufficient condition for validity of the First Finitistic Dimension Conjecture that extends the well-known result of Huisgen-Zimmermann and Smalø.

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