JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (10): 7-10.doi: 10.6040/j.issn.1671-9352.0.2014.332

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Copure projective dimensions under Hopf extensions

CHEN Xiu-li, CHEN Jian-long   

  1. Department of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China
  • Received:2014-07-15 Online:2014-10-20 Published:2014-11-10

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Abstract: Let H be a finite dimensional Hopf algebra and A be an algebra over a fixed field k. It is proved that the left copure projective dimension of A＃H and that of A is the same when H is semisimple and the extension A/AH is H*-Galois. Moreover, it is shown that A＃H is QF if and only if A is QF. Using (co)induction functors, we study the relations between copure projective dimensions in A＃H-Mod and the counterparts in AH-Mod.

Key words: Hopf extension, copure projective dimension, QF ring

CLC Number: 

  • O153.3
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