Exploring EADS Modules: Properties, Direct Sums, and Applications in Matrix Rings

Abstract

We introduce the concept of an EADS module, defined such that for any decomposition M=A circle plus B and any ec-complement C of A in M, the module satisfies M=A circle plus C. This study explores the properties of EADS modules and examines their relationships with other established properties. We particularly investigate the behavior of EADS modules concerning direct sums and direct summands. In addition, we present applications, including matrix rings over a right EADS ring.