L-Modules

Abstract

In this paper, considering L-algebras, which include a significant number of other algebraic structures, we present a definition of modules on L-algebras (L-modules). Then we provide some examples and obtain some results on L-modules. Also, we present definitions of prime ideals of L-algebras and L-submodules (prime L-submodules) of L-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime L-submodules.

Keywords

• \(l\)-algebra
• \(l\)-module
• \(l\)-submodule
• prime \(l\)-submodule