Rees matrix rings (original) (raw)

This article explores the connections between semigroup theory and ring theory, focusing specifically on the Rees matrix rings. The examination of these mathematical structures involves understanding their relationships with completely O-simple semigroups and simple rings with minimal one-sided ideals. Through definitions, propositions, and theoretical applications, the paper delineates the properties of semi-linear transformations and adjoint mappings in the context of dual pairs of modular systems, ultimately revealing insights into their continuity and rank-related characteristics.