弱Ding-投射模及相关维数

Weak Ding-projective Modules and Related Dimensions

利用同调代数的方法,讨论关于半对偶模C的弱Ding-投射模的若干性质,证明弱Ding PP_(C)-分解的每个核都是弱Ding-投射模.研究模M的弱Ding-投射维数wDP_(C)-pd(M)小于等于n的若干等价刻画.结果表明:wDP_(C)-pd(M)≤n,当且仅当对任意C-f-投射模N都有Ext_(R)^(j≥n+1)(M,N)=0,当且仅当对任意C-f-投射维数有限的模N都有Ext_(R)^(j≥n+1)(M,N)=0,当且仅当存在正合列0→K_(n)→W_(n-1)→…→W_(1)→W_(0)→M→0,其中W_(i)(0≤i≤n-1)和K_(n)是弱Ding-投射模.

Using methods of homological algebra,some properties of weak Ding-projective modules with respect to a semidualizing module C are discussed.It is proved that every kernel of weak Ding PP_(C)-resolution is weak Ding-projective module.Some equivalent characterizations of wDP_(C)-pd(M)are equal or less than n,in which wDP_(C)-pd(M)≤n denotes the weak Ding-projective dimension of module M.The results indicate that:wDP_(C)-pd(M)≤n if and only if Ext_(R)^(j≥n+1)(M,N)=0 for any C-f-projective module N,if and only if Ext_(R)^(j≥n+1)(M,N)=0 for any module N with finite C-f-projective dimension,if and only if there exists an exact sequence0 → K_(n)→W_(n-1)→…→W_(1)→W_(0)→M→0 with W_(i)(0≤i≤n-1)and K_(n) weak Ding-projective modules.