Gorenstein Flat Modules of Hopf-Galois Extensions

Let A/B be a right H-Galois extension over a semisimple Hopf algebra H. The purpose of this paper is to give the relationship of Gorenstein flat dimensions between the algebra A and its subalgebra B, and obtain that the global Gorenstein flat dimension and the finitistic Gorenstein flat dimension of A is no more than that of B. Then the problem of preserving property of Gorenstein flat precovers for the Hopf-Galois extension will be studied. Finally, more relations for the crossed products and smash products will be obtained as applications.

Automated summary

This paper investigates the relationship of Gorenstein flat dimensions between the algebra A and its subalgebra B in a right H-Galois extension A/B over a semisimple Hopf algebra H. It is found that the global Gorenstein flat dimension and the finitistic Gorenstein flat dimension of A is no more than that of B. The problem of preserving property of Gorenstein flat precovers for the Hopf-Galois extension is then studied. Finally, more relations for the crossed products and smash products are obtained as applications.