ON HOPF GALOIS HIRATA EXTENSIONS
Let H be a finite-dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*-Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB(BH)#H. A sufficient condition is also given for B to be an H*-Galois Azumaya extension of BH.
Azumaya Extensions and Galois Correspondence
For H a finite-dimensional Hopf algebra over a field k, we study H*-Galois Azumaya extensions A, i.e., A is an H-module algebra which is H*-Galois with A/AH separable and AH Azumaya. We prove that there is a Galois correspondence between a set of separable subalgebras of A and a set of separable subalgebras of CA(AH), thus generalizing the work of Alfaro and Szeto for H a group algebra. We also study Galois bases and Hirata systems.
Meromorphic function sharing a small function with a homogeneous differential polynomial
Abstract In this paper, we consider a Brück-type result for a homogeneous differential polynomial generated by a meromorphic function.