中文摘要：

研究了环扩张下的Gorenstein平坦模型结构及其同伦范畴．设R≤S是满足一些条件的平坦扩张．我们证明了若．f：M→N在S-模范畴的Gorenstein平坦模型结构中是上纤维化（纤维化，弱等价），则f：M→N在R模范畴中亦如此；若R≤S是优越扩张，反过来也成立，即在优越扩张下Gorenstein平坦模型结构是不变的．进而，相关的稳定范畴是等价的，当且仅当对任意Gorenstein平坦S-模M，Coker（η／M）是平坦的，其中η表示S-模范畴和R-模范畴间的Quilten伴随函子的单位．

英文摘要：

The Gorenstein flat model structures and resulting homotopy categories under extensions of rings are studied. Along the flat extension R 〈 S satisfying a few conditions, we show that if f ： M → N is a cofibration （resp. fibration, weak equivalence） in the Gorenstein flat model structure of S-Mod, then f is so in R-Mod; furthermore, the converse holds if R 〈 S is an excellent extension. That is, Gorenstein fiat model structure are invariant under excellent extensions. Moreover, the associated stable categories are equivalent if and only if Coker（ηM） is flat for any Gorenstein flat S-module M, where η is unit of the Quillen adjunction between S-Mod and R-Mod.