2021/02/01 by Gangyong Lee, Lee, Gangyong, Mauricio Medina-Bárcenas +1
Mathematics · #16D40 #16D50 #16E50 #16E60 #16S50 #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2102.01014
openalex publication_date 2021/02/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In this article, we study the notion of a finite Σ-Rickart module, as a module theoretic analogue of a right semi-hereditary ring. A module M is called finite Σ-Rickart if every finite direct sum of copies of M is a Rickart module. It is shown that any direct summand and any direct sum of copies of a finite Σ-Rickart module are finite Σ-Rickart modules. We also provide generalizations in a module theoretic setting of the most common results of semi-hereditary rings. Also, we have a characterization of a finite Σ-Rickart module in terms of its endomorphism ring. In addition, we introduce M-coherent modules and provide a characterization of finite Σ-Rickart modules in terms of M-coherent modules. At the end, we study when Σ-Rickart modules and finite Σ-Rickart modules coincide. Examples which delineate the concepts and results are provided.