X-丁投射模

X-Ding projective modules

设R是具有单位元的结合环,X是包含所有平坦模的R-模类.引入X-丁投射模和X-丁投射维数的定义并研究了相关性质.如果存在正合列P=∶…→P1→P0→P0→P1→…,其中Pi,Pi是投射模,i∈Z,对于任意R-模F∈X,HomR(-,F)作用在正合列P上保持正合,并且M=Ker(P0→P1),那么称M是X-丁投射模.证明了X-丁投射模类是投射可解的并且X-丁投射模保持直和与直和项,同时证明了若GX-Dpd(R)<∞,则(X-DP(R),(X-DP(R))⊥)是完备遗传余挠对.

Let R be an associative ring with identity and X is a class that contains all flat R-modules,the definitions of X-Ding projective modules and X-Ding projective dimensions are introduced and the relative properties are studied.A right R-module M is called X-Ding projective if there exists an exact sequence P=∶…→P1→P0→P0→P1→…of projective right R-modules such that M=Ker(P0→P1)and HomR(P,F)is exact whenever F∈X.It is proved that the class of all X-Ding projective modules is projectively resolving and is closed under direct sums and direct summands.In addition,it is proved that if GX-Dpd(R)<∞,then(X-DP(R),(X-DP(R))⊥)is a complete here ditary cotorsion pair.