Gorenstein Flat Modules of Hopf-Galois Extensions

Abstract

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.

Keywords

• Hopf-Galois extension
• Gorenstein flat module
• global Gorenstein flat dimension
• Finitistic Gorenstein flat dimension
• Gorenstein flat precover