Akademik Veri Yönetim Sistemi
ASES V. INTERNATIONAL VAN SCIENTIFIC RESEARCH CONGRESS , Van, Türkiye, 8 - 10 Ağustos 2025, ss.300-306, (Tam Metin Bildiri)
In this study, we investigate the structural interplay between two significant notions in module theory: coatomic modules and modules possessing the summand sum property (SSP). While both concepts are independently well-studied in the literature, a detailed examination of their mutual influence remains limited. Our aim is to bridge this gap by identifying conditions under which coatomicity ensures the SSP, and conversely, when the SSP leads to coatomic behavior. We begin by recalling essential definitions and known results regarding coatomic modules, characterized by the condition that every proper submodule is contained in a maximal submodule. We then proceed to revisit the SSP, which ensures that the sum of any two direct summands of a module remains a direct summand. The significance of this property lies in its implications for module decompositions and the behavior of projections and homomorphic images. Our main results provide several necessary and sufficient conditions relating these two properties. The theorems are supported by detailed proofs and accompanied by illustrative examples that highlight both the interaction and the independence of the two concepts. We also offer counterexamples to demonstrate the boundaries of the implications, thereby providing a sharper understanding of the structure of modules satisfying either or both properties. Through this investigation, we aim to enrich the theory of direct sum decompositions by clarifying how coatomicity and the summand sum property coexist or diverge within module classes. The results contribute to a deeper comprehension of module structure and open the door to further generalizations in the context of lifting, extending, and continuous modules.