DUALIZING MODULES AND n-PERFECT RINGS
DUALIZING MODULES AND n-PERFECT RINGS
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DOI：
10.1017/s0013091503001056
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发表时间：
2005-02
影响因子：
0.7
通讯作者：
E. Enochs;Overtoun M. G. Jenda;J. A. López-Ramos
中科院分区：
文献类型：
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作者：
E. Enochs;Overtoun M. G. Jenda;J. A. López-Ramos
摘要本文将Gorenstein模和Foxby对偶的结果推广到非交换情形。这是在§3中完成的，在那里我们刻画了Auslander和Bass类，每当我们有一个与一对环相关联的对偶模时，它们就会出现。在这种情况下，已知平坦模具有有限的投射维数。由于环的这一性质本身就很有意义，我们在本文的第2节中专门讨论这类环。最后，在本文的最后一节，我们考虑了Gorenstein模概念的自然推广，它出现在§3的情况下，即当我们有一个对偶模时。AMS 2000数学科目分类：小学16年级D20
Abstract In this article we extend the results about Gorenstein modules and Foxby duality to a non-commutative setting. This is done in §3 of the paper, where we characterize the Auslander and Bass classes which arise whenever we have a dualizing module associated with a pair of rings. In this situation it is known that flat modules have finite projective dimension. Since this property of a ring is of interest in its own right, we devote §2 of the paper to a consideration of such rings. Finally, in the paper’s final section, we consider a natural generalization of the notions of Gorenstein modules which arises when we are in the situation of §3, i.e. when we have a dualizing module. AMS 2000 Mathematics subject classification: Primary 16D20