关于倾斜对的余挠理论

Cotorsion theories relative to tilting pairs

设(C,T)是Artin代数Λ上的一个倾斜对.利用同调代数的方法,讨论了关于(C,T)的预覆盖和预包络.结果表明当modΛGen(C)且eΛ(C,-)<∞时,(⊥1(T⊥),T⊥)是一个完全遗传余挠理论,其中Gen(C)表示由C生成的模类,eΛ(C,-)=sup eΛ(C,M)|M∈modΛ且eΛ(C,M)=sup i∈N|Ext^iΛ(C,M)≠0.

Let(C,T)be a tilting pair over an Artin algebraΛ.Using methods of homological algebra,the precovers and preenvelopes relative to tilting pair(C,T)are discussed.The results indicate that(⊥1(T⊥),T⊥)is a complete hereditary cotorsion theory when modΛGen(C)and eΛ(C,-)<∞,where Gen(C)denotes the class of modules generated by C,eΛ(C,M)=sup i∈N Ext^iΛ(C,M)≠0 and eΛ(C,-)=sup eΛ(C,M)M∈modΛ.