On SCI-modules

Abstract

Let R be a commutative ring with unity 1 ≠ 0 and M a unitary left R-module. In this paper, we introduce the SCI-modules which is an extension of SCI-rings studied in [4]. The aim of this article comes from to the following point. Let ℤ be the ring of integers and M = ⊕ ℤ ∕ pℤ a ℤ-module with p a prime number. It is easy to see that M ∈ σ[ℤ] is co-Hopfian but it is not finitely cogenerated. An R-module M is said to be a SCI-module if any co-Hopfian object of σ[M] is finitely cogenerated. Firstly, we give some properties of SCI-modules. After that, we give two theorems of characterizations.