2023/06/02 by Abderrahim El Moussaouy, Moussaouy, Abderrahim El
Mathematics · #16D10 #16D40 #16D90 #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2306.01883
openalex publication_date 2023/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main aim of this paper is the Hopficity of module classes, the study of modules (rings) by properties of their endomorphisms is a classical research subject. In 1986, Hiremath \citeHi introduced the concepts of Hopfian modules and rings, the notion of Hopfian modules are defined as a generalization of modules of finite length as the modules whose surjective endomorphisms are isomorphisms. Later, the dual concepts co-Hopfian modules and rings were given. Hopfian and co-Hopfian modules (rings) have been investigated by several authors. For example, Hiremath \citeHi, Varadarajan \citeVa, \citeVa1, Xue \citeXu, Haghany \citeHag, Liu \citeLi, and Yang and Liu \citeYl. In 2001, Haghany and Vedadi \citeHa, and in 2002, Ghorbani and Haghany \citeGh, respectively, introduced and investigated the weakly co-Hopfian and generalized Hopfian modules. These modules and several generalizations of them are extensively studied also by several authors.