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