优越扩张下的⊥RW-Gorenstein投射性

⊥RW-Gorenstein projectiveness under excellent extensions

对于环的优越扩张R S,一个R-模M是一个广义倾斜模,则SS■RW也是一个广义倾斜模.此外,相对于一个广义的倾斜模RW,文中定义了⊥RW-Gorenstein投射模,并证明了在环的优越扩张下,这类模的⊥RW-Gorenstein投射模性是保持的,即对于环的优越扩张R S和S-模SM,R M是一个⊥RW-Gorenstein投射模当且仅当SM是一个⊥SS RW-Gorenstein投射模.

For an excellent extension R<S,if RM is a generalized tilting module,then SS■RW is also a generalized module.Furthermore,we define the ⊥RW-Gorenstein module respect to a generalized module RW,and prove that the ⊥RW-Gorenstein projective module is retentive under excellent extensions,that is,for an excellent extension R<S and an S-module SM,RM is ⊥RW-Gorenstein projective if and only if SM is ⊥SS■RW-Gorenstein projective.