Rough Anti-Ideals in Semirings

Abstract

In this paper, the notion of rough anti-ideals and proposal the of an extension of the conventional theory in semirings are studied. We provide illustrative examples to clarify our definitions and explore structural properties related to rough anti-ideals. We examine the concept of rough anti-ideals in semirings in detail and contribute to the theoretical development of rough set theory as applied to the algebraic structure of semirings. We use the congruence relations and thoroughly analyze them to understand the properties of left and right anti-ideals and the associated algebraic structures. We try to find ways to advance theoretical and applied research by clarifying the properties and relationships between rough anti-ideals and semirings. Despite these advancements, there remain numerous properties and directions yet to be explored. Investigating the behavior and applications of rough anti-ideals in diverse mathematical and real-world contexts offers significant potential for further study. Additionally, examining the connections between rough anti-ideals and other algebraic structures could lead to new discoveries and foster cross-disciplinary collaboration.By utilizing congruence relations and thoroughly analyzing the properties of left Furthermore, we examine the relationships between algebraic structures involving rough anti-ideals and semirings, focusing on their theoretical foundations. We aim to clarify these concepts and investigate their potential applications in theoretical and practical contexts.