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REGULARITY AND IDEALS IN NEAR-SEMIRINGS
Keywords:
semiring, near-semiring, regular, idempotent, idealAbstract
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.
Received: December 5, 2022
Accepted: January 12, 2023
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