On prime ideals on a semi-ring associated with a nexus

In this study, we explore prime ideals and prime elements within a semi-ring constructed over a nexus. We characterize these elements using panels and quasi-panels. Furthermore, we establish conditions under which a semi-ring associated with a nexus N becomes unitary. The concept of homomorphism for these semi-rings is introduced, and several of their properties are examined. Additionally, by analyzing their characteristics, we demonstrate that a quotient semi-ring can be induced by an ideal of a semi-ring over a nexus, and localization is successfully defined. To illustrate these concepts, we provide specific examples.

کلیدواژه ها:

(prime) Ideal ، Localization ، Nexus ، Prime element ، Semi-ring