Tilting modules and Gorenstein rings
Tilting modules and Gorenstein rings
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DOI：
10.1515/forum.2006.013
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发表时间：
2006-03
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影响因子：
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通讯作者：
Lidia Angeleri Hügel;Dolors Herbera;J. Trlifaj
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文献类型：
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作者：
Lidia Angeleri Hügel;Dolors Herbera;J. Trlifaj
摘要 我们应用倾斜理论来研究有限射影维数的模。我们分别为模块的倾斜类和共倾斜类引入有限和余有限类型的概念，表明对于每个维度，这些类和模块的解析类之间存在双射。然后我们关注 Iwanaga-Gorenstein 环。利用倾斜理论，我们证明了这些环的第一个有限维猜想。此外，我们通过 Gorenstein 单射模形成倾斜类的性质将它们描述在诺特环中。最后，我们给出一维交换 Gorenstein 环的（共）有限型（共）倾斜模族的显式构造。
Abstract We apply tilting theory to study modules of finite projective dimension. We introduce the notion of finite and cofinite type for tilting and cotilting classes of modules, respectively, showing that, for each dimension, there is a bijection between these classes and resolving classes of modules. We then focus on Iwanaga-Gorenstein rings. Using tilting theory, we prove the first finitistic dimension conjecture for these rings. Moreover, we characterize them among noetherian rings by the property that Gorenstein injective modules form a tilting class. Finally, we give an explicit construction of families of (co)tilting modules of (co)finite type for one-dimensional commutative Gorenstein rings.