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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 &rarr M &rarr UI &rarr N &rarr 0 with M ∈ Copres∞(U) and I is a set, N ∈ Copres∞(U) is equivalent to ExtR1(N, U) &rarr ExtR1(UI, U) is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0 &rarr L &rarr M &rarr N &rarr 0 with L, N ∈ Copres∞(U), N ∈ Copres∞(U) is equivalent to the induced sequence 0 &rarr ▵(N) &rarr ▵(M) &rarr ▵(L) &rarr 0 which is exact if and only if U induces a duality ▵US: ⊥US ⇔ Copres∞(U): ▵RU. Moreover, U is a co-*n-module if and only if U is a co-*∞-module and Copres∞(U)=Copresn(U).
- 出版日期2010
- 单位东南大学
