Akademik Veri Yönetim Sistemi
Journal of Algebra and its Applications, 2025 (SCI-Expanded, Scopus)
Using the notion of relative max-projectivity, max-projectivity domain of a module is investigated. Such a domain includes the class of all modules whose maximal submodules are direct summands (this class denoted as MDMod -R). We call a module max- p-poor if its max-projectivity domain is exactly the class MDMod -R. We establish the existence of max- p-poor modules over any ring. Furthermore, we study commutative rings whose simple modules are projective or max- p-poor. Additionally, we determine the right Noetherian rings for which all right modules are projective or p-poor. Max- p-poor abelian groups are fully characterized and shown to coincide precisely with p-poor abelian groups. We also further investigate modules that are max-projective relative to themselves, which are known as simple-quasi-projective modules. Several properties of these modules are provided, and the structure of certain classes of simple-quasi-projective modules is determined over specific commutative rings including the ring of integers and valuation domains.