journal6 ›› 2012, Vol. 33 ›› Issue (2): 1-6.DOI: 10.3969/j.issn.1007-2985.2012.02.001

• Mathematics •     Next Articles

Auslander-Reiten Translations for Comodules


  1. (1.Department of Mathematics,Chaohu College,Hefei 238000,China;2.School of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China;3.School of Mathematics,Hunan Institute of Science and Technology,Yueyang 414000,Hunan China)
  • Online:2012-03-25 Published:2012-05-28

Abstract: Let  Γ be a coalgebra over a field k.Further discussion of the functor  τ=DTr:MΓqc→ MΓqc is carried out,where MΓqc denotes the full subcategory of MΓ determined by the quasi-finitely copresented comodules.If  Γ is a semisimple coalgebra,it is proved that  the functor  τ:f.d.M〖TXX-〗Γqc→ f.d.M〖TX-〗Γqp is a categories equivalence,where M〖TXX-〗Γqc (MΓqp)  is the injectively (projectively) stable category and f.d.M〖TXX-〗Γqc(f.d.MΓqp) is the full subcategory of  M〖TXX-〗Γqc (M〖TX-〗Γqp) determined by the finite dimensional injective(projective) comodules.

Key words: coalgebra, comodule, transpose, translation

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