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

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Islamic Azad University of Kerman, Kerman, Iran

2 Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran

Abstract

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.

Keywords

References

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Algebraic Structures and Their Applications

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