Acta Mathematica Sinica, English Series

, Volume 33, Issue 11, pp 1569–1577 | Cite as

Avramov–Martsinkovsky type exact sequences with tor functors

Article

Abstract

For two classes of right R-modules W, X such that PWX, where P is the class of projective right R-modules, we show that there is an Avramov–Martsinkovsky type exact sequence with generalized Tate homology functor \({\widehat {Tor}^{X.W}}\), relative homology functors Tor W and Tor X . Many results in Iacob [Comm. Algebra, 35, 1589–1606 (2007)] and Liang [Algebr. Represent. Theory, 16, 1541–1560 (2013)] are generalized and improved.

Keywords

Relative homology (generalized) Tate homology Avramov–Martsinkovsky type exact sequence 

MR(2010) Subject Classification

16E10 16E30 18G10 18G25 

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Notes

Acknowledgements

The authors are grateful to the referee for several corrections, improvements in exposition, and a more general statement of the main result.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesChongqing Normal UniversityChongqingP. R. China
  2. 2.School of Mathematics and PhysicsLanzhou Jiaotong UniversityLanzhouP. R. China

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