摘要
利用同调代数的方法,讨论D_(C)-内射模的若干性质,证明I_(C)(R)是DI_(C)(R)的投射生成子,其中DI_(C)(R)表示所有D_(C)-内射R-模组成的类,I_(C)(R)表示所有形如Hom R(C,E)(E为内射模)的R-模组成的类.借助投射生成子这一工具,研究DI_(C)(R)-投射维数小于等于n的若干等价刻画,及短正合列0→L→M→N→0中各项DI_(C)(R)-投射维数之间的关系.
Using methods of homological algebra,some properties of D_(C)-injective modules are discussed,it is proved that I_(C)(R)is a projective generator of DI_(C)(R),where DI_(C)(R)denotes the class of all D_(C)-injective R-modules,I_(C)(R)denotes the class of all R-modules Hom R(C,E)with E injective.With the help of projective generator tool,the paper investigates some equivalent characterizations of DI_(C)(R)-projective dimension less than or equal to n,and relationships between DI_(C)(R)-projective dimensions of each term in the short exact sequence 0→L→M→N→0.
作者
何东林
HE Dong-lin(School of Mathematics and Information Science,Longnan Teachers College,Longnan 742500,China)
出处
《青海师范大学学报（自然科学版）》
2021年第1期13-18,共6页
Journal of Qinghai Normal University(Natural Science Edition)
基金
甘肃省高等学校创新基金项目(2020A-227)。
