In this paper, we investigate conditions that force regular near-semirings (additive or multiplicative regular near-semirings) to be idempotent (additive idempotent). In addition, we study some kinds  of ideals as p-ideals and subtractive ideals in near-semirings and investigate their properties in near-semirings. Finally, we define two congruence relations on a near-semiring, and an additive inverse regular near-semiring, respectively. Then we give constructions of quotient near-semirings induced by congruence relations.

semiring, near-semiring, regular, idempotent, ideal.

Received: December 5, 2022; Accepted: January 12, 2023; Published: January 27, 2023

How to cite this article: Utsanee Leerawat and Benya Setthanarak, Regularity and ideals in near-semirings, JP Journal of Algebra, Number Theory and Applications 60(1) (2023), 39-57. http://dx.doi.org/10.17654/0972555523003 

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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