Abstract

Let U be a nonempty set of R-modules and V be a submodule of ⊕_ʌU_λ, U_λ∈U for all λ∈Λ. A U_V generated module is a generalization of U-generated module by using the concept of V-coexact sequence. We say that an R-module N is generated by U_V if there is an epimorphism from V to N. In this paper, we introduce the definition of rank of U_V-generated modules. Furthermore, we investigate some properties of rank of UV-generated modules.

Highlights

  • Let R be a ring and let A f →− gB →− C be an exact sequence of R-modules, i.e. Im f = Ker g(= g−1(0)).This exact sequence can be generalized to a quasi-exact sequence by replacing the submodule 0 with any submodule U ⊆ C (Davvaz and Parnian-Garamaleky, 1999)

  • We introduce the definition of rank of UV -generated modules

  • We introduce the definition of the rank of UV -generated modules, and we investigate some properties of the rank of UV -generated modules

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Summary

Introduction

Let U be a nonempty set of R-modules and V be a submodule of ⊕ΛUλ, Uλ ∈ U for all λ ∈ Λ. We investigate some properties of rank of UV -generated modules. A sub-exact sequence is used to establish the X-sub-linearly independent module as a generalization of linearly independent module relative to a family of R-modules (Fitriani et al, 2017).

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