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Paper   IPM / M / 16864
School of Mathematics
  Title:   A study of Tate homology via the approximation theory with applications to the depth fomula
1.  Arash Sadeghi
2.  Tirdad Sharif (Joint with O. Celikbas and L. Liang)
  Status:   Published
  Journal: Acta Math. Sin. (Engl. Ser.)
  Vol.:  39
  Year:  2023
  Pages:   439-458
  Supported by:  IPM
In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part of the paper we generalize a result of Avramov and Martsinkovsky by using the Auslander-Buchweitz approximation theory, and obtain a new exact sequence connecting absolute Tor modules with relative and Tate Tor modules. In the second part of the paper we consider a depth equality, called the depth formula, which has been initially introduced by Auslander and developed further by Huneke and Wiegand. As an application of our main result, we generalize a result of Yassemi and give a new sufficient condition implying the depth formula to hold for modules of finite Gorenstein and finite injective dimension.

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