Frobenius Pairs And Their Applications

In this paper,we mainly studies some properties and applications of Frobenius pairs.First of all,we study the applications of Frobenius pairs in Gorenstein projective dimension and Gorenstein flat dimension,in particular,we improve some classical results by Holm.Next,we define syzygy objects with respect to Frobenius pairs and study some properties of the syzygy objects.At the same time,we study some applications of Frobenius pairs relative to Gorenstein syzygy modules and get some results of Huang et al.about Gorenstein syzygy modules.Finally,we define Gorenstein flat syzygy modules and study some properties of Gorenstein flat syzygy modules.