Tilting theory and the finitistic dimension conjectures
Tilting theory and the finitistic dimension conjectures
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DOI：
10.1090/s0002-9947-02-03066-0
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发表时间：
2002-06
影响因子：
1.3
通讯作者：
Lidia Angeleri-Hugel;J. Trlifaj
中科院分区：
文献类型：
--
作者：
Lidia Angeleri-Hugel;J. Trlifaj
设R是右Noetherian环，P<∞是有限投射维数的n-表现模类.证明了findimR = n < ∞当且仅当存在（无限生成的）倾斜模T使得pdT = n且T ∈ =（p<∞）∈.若R是Artin代数，则T可被认为是逆生成的当且仅当p<∞是逆变有限的.我们还得到了第一维猜想成立的一个充分条件，推广了Huisgen-Zimmermann和Smalo的著名结果.
Let R be a right noetherian ring and let P<∞ be the class of all finitely presented modules of finite projective dimension. We prove that findimR = n < ∞ iff there is an (infinitely generated) tilting module T such that pdT = n and T⊥ = (p<∞)⊥. If R is an artin algebra, then T can be taken to be finitely generated iff p<∞ 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 Smalo.