An artin algebra is called CM-free provided that all its finitely generated Gorenstein projective modules are projective. We show that a connected artin algebra with radical square zero is either… (More)

Article history: Received 9 April 2009 Available online 17 September 2010 Communicated by Luchezar L. Avramov Dedicated to Professor Claus Michael Ringel on the occasion of his sixty-fifth birthday… (More)

We study positively-graded Hopf algebras and obtain (dual) Gabriel-type results on graded Hopf algebras. Using it, we get certain (non-degenerate) graded Hopf pairings between quantum symmetric… (More)

We prove that if a positively-graded ring R is Gorenstein and the associated torsion functor has finite cohomological dimension, then the corresponding noncommutative projective scheme Tails(R) is a… (More)

We give a short proof of the tilting theorem by Happel, Reiten and Smalø: two abelian categories A and B are derived equivalent, provided that B is tilted from A.

We prove that in an abelian category with enough projective objects, the extension subcategory of two covariantly finite subcategories is still covariantly finite. This extends a result by Sikko and… (More)

This paper consists of three results on Frobenius categories: (1)we give sufficient conditions on when a factor category of a Frobenius category is still a Frobenius category; (2) we show that any… (More)

Article history: Received 20 March 2009 Available online 9 June 2009 Communicated by Michel Van den Bergh Dedicated to Professor Helmut Lenzing on the occasion of his seventieth birthday