优越扩张下G C-投射模

G C-projective Modules under Excellence Extension

在半对偶模的基础上,针对一个模的G C-投射性在环的优越扩张下是保持的,在已知结论正确的情况下采用不同于以往的证明方法,利用模的G C-投射性的等价命题证明主要结论,即对于环的优越扩张R→S和S-模S M,R-模R M是一个G C-投射模当且仅当S M是一个G S RC-投射模。使用等价命题后采用的新证明方法逻辑清晰,形式统一,便于模的具体相关性质的推广与应用。

We know that the Gorenstein projectivity relative to a semidualizing module is preserved under excellent extensions.A new method of proof is adopted when the conclusion is known to be correct.Using the equivalent proposition of the definition to prove that for an excellent extension R→S and an S-module S M,R M is G C-projective module if and only if S M is G S RC-projective module.The form of the new method after using equivalent proposition is uniform.It is convenient to generalize and apply the related properties of modules.