相对余挠自由模和对偶Auslander转置的若干注记  

Some Notes of Relative Cotorsionfree Modules and the Dual Auslander Transpose

作　　者：何东林[1] HE Donglin(School of Mathematics and Information Sciences,Longnan Teachers College,Longnan 742500,China)

机构地区：[1]陇南师范高等专科学校数信学院,甘肃陇南742500

出　　处：《湖北民族大学学报（自然科学版）》2020年第4期437-440,共4页Journal of Hubei Minzu University:Natural Science Edition

基　　金：甘肃省高等学校创新能力提升项目(2019B-224);甘肃省高等学校创新基金项目(2020A-277).

摘　　要：利用同调代数和环模理论的方法,给出n-C-余挠自由模和对偶Auslander转置的若干性质和刻画,并证明了M是n-C-余挠自由模,当且仅当存在Hom R(C,-)下正合的正合列A n-1→…→A 1→A 0→M→0,其中A i∈Add(R C)(0≤i≤n-1),当且仅当存在Hom R(C,-)下正合的正合列C S P n-1→…→C S P 1→C S P 0→M→0,其中P i(0≤i≤n-1)是投射左S-模.研究短正合列0→L→M→N→0中各项的n-C-余挠自由性之间的关系.结果表明:如果L和M是n-C-余挠自由模,那么N是n-C-余挠自由模;如果L和N是n-C-余挠自由模,那么M是n-C-余挠自由模;如果M是n-C-余挠自由模且N是(n+1)-C-余挠自由模,那么L是n-C-余挠自由模.Using methods of homological algebra and theories of rings and modules,some properties and characterizations of n-C-cotorsionfree modules and the dual Auslander transpose are gived,and it is proved that M is a n-C-cotorsionfree module,if and only of there exists a Hom R(C,-)-exact exact sequence A n-1→…→A 1→A 0→M→0 with A i∈Add(R C)(0≤i≤n-1),if and only of there exists a Hom R(C,-)-exact exact sequence C S P n-1→…→C S P 1→C S P 0→M→0 with P i(0≤i≤n-1)projective left S-modules.The relationships between n-C-cotorsionfree property of each term in the short exact sequence 0→L→M→N→0 are investigated.The results indicate that:if L and M are n-C-cotorsionfree modules,then N is n-C-cotorsionfree module;if L and N are n-C-cotorsionfree modules,then M is n-C-cotorsionfree module;if M is n-C-cotorsionfree module and N is(n+1)-C-cotorsionfree module,then L is n-C-cotorsionfree module.

关 键 词：n-C-余挠自由模 C-余自反模 半对偶模 Auslander转置 

分 类 号：O154[理学—数学]