A generalization of co-*~n-modules  

余星n模的推广(英文)

作　　者：姚玲玲[1] 陈建龙[1] 

机构地区：[1]东南大学数学系,南京211189

出　　处：《Journal of Southeast University(English Edition)》2010年第3期505-508,共4页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China (No.10971024);Specialized Research Fund for the Doctoral Program of Higher Education (No.200802860024)

摘　　要：A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copres∞（U）. A module U is a co-＊∞-module if and only if U is co-selfsmall and for any exact sequence 0→M→UI→N→0 with M∈Copres∞（U） and I is a set, N∈Copres∞（U） is equivalent to Ext1R（N,U）→Ext1R（UI,U） is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0→L→M→N→0 with L, N∈Copres∞（U）, N∈Copres∞（U） is equivalent to the induced sequence 0→Δ（N）→Δ（M）→Δ（L）→0 which is exact if and only if U induces a duality ΔUS：⊥USCopres∞（U）：ΔRU. Moreover, U is a co-＊n-module if and only if U is a co-＊∞-module and Copres∞（U）=Copresn（U）.如果一个模余自小和无穷拟内射称其为余星无穷模.研究了其性质及等价刻画.当一个模为余星无穷模时,函子HomRU(-,U)在Copres∞(U)中正合.一个模是余星无穷模当且仅当U余自小,对任意的正合列0→M→UI→N→0满足M∈Copres∞(U)且I是一个集合,N∈Copres∞(U)等价于ExtR1(N,U)→Ext1R(UI,U)是一个单同态当且仅当U余自小并且对于任意的正合列0→L→M→N→0满足L,N∈Copres∞(U),N∈Copres∞(U)等价于导出的列0→Δ(N)→Δ(M)→Δ(L)→0是正合的当且仅当U通过函子ΔUS和ΔRU导出了子范畴⊥US和Copres∞(U)之间的对偶.并且证明了一个模为余星n模当且仅当它是余星无穷模且Copres∞(U)=Copresn(U).

关 键 词：co-＊∞-module ∞-quasi-injective co-selfsmall co-＊n-module 

分 类 号：O154.2[理学—数学]