On the Generalized Supplemented Lattices and Radicals Module

Rathod D P, Wadbude R S

Abstract: This paper investigates the interplay between the lattice of submodules and the property of being (amply) supplemented. We introduce a new class of modules, termed generalized supplemented modules, defined via a closure operator on the submodule lattice linked to the Jacobson radical. We characterize these modules and provide necessary and sufficient conditions for a module to be generalized supplemented. Furthermore, we explore the behavior of this property under direct sums and homomorphic images, generalizing several key results from the classical theory of supplemented modules established by Kasch and Mares [1], Wisbauer [2], and others. Our results unify and extend significant theorems in the literature, providing a fresh lattice-theoretic perspective on supplementation.

Keywords: Supplemented modules, radical submodules, Jacobson radical, lattice of submodules, closure operators, module theory

How to Cite?: Rathod D P, Wadbude R S, "On the Generalized Supplemented Lattices and Radicals Module", Volume 14 Issue 9, September 2025, International Journal of Science and Research (IJSR), Pages: 28-30, https://www.ijsr.net/getabstract.php?paperid=SR25901194600, DOI: https://dx.doi.org/10.21275/SR25901194600