MMN-4745
BKN rings: A study of nonzero homomorphisms between modules and some applications to homological algebra
Gerardo Reyna Hernández; Iván Fernando Vilchis Montalvo; Luis Donaldo Arreola Bautista; Martha Lizbeth Shaid Sandoval Miranda;Abstract
In this paper, we study BKN rings, which are rings that satisfy the property
Hom_{R}(M,N)≠0 for all nonzero left (right) R-modules M and N. Our aim is to provide a comprehensive overview of BKN rings and their connections to other types of rings, such as retractable and completely coretractable rings, commutative rings, and their connections to injective R-modules and nontrivial torsion theories. We prove several results, including the left-right symmetry of the BKN property and its preservation under various ring operations. Furthermore, we explore the relationship between BKN rings and the tensor product of modules. Our study provides insight into the comprehensive understanding of BKN rings, providing information about the relation between
BKN rings and the Tor, Ext, and ext functors.
Vol. 26 (2025), No. 2, pp. 813-823