We generalize the homological characterization of sequentially Cohen-Macaulay modules over a graded Gorenstein algebra to sequentially reflexive modules over Noetherian, not necessarily commutative rings, with a N-partial cotilting bimodule playing the role of the graded Gorenstein algebra. In such a way we get a complete version of the "Cotilting Theorem". Finally, conditions are found to insure that the "N-partial cotilting notion" pass through a finite ring extension.
Sequentially reflexive modules
TONOLO, ALBERTO
2004
Abstract
We generalize the homological characterization of sequentially Cohen-Macaulay modules over a graded Gorenstein algebra to sequentially reflexive modules over Noetherian, not necessarily commutative rings, with a N-partial cotilting bimodule playing the role of the graded Gorenstein algebra. In such a way we get a complete version of the "Cotilting Theorem". Finally, conditions are found to insure that the "N-partial cotilting notion" pass through a finite ring extension.
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