Near-ring congruences on seminearrings.

While establishing the bijection between near-ring congruences and various types of ideals of seminearrings, different kinds of restrictions were imposed either on the seminearrings under consideration or on the near-ring congruences. In this paper we consider a seminearring S without any restriction and establish that there exists an inclusion preserving bijective correspondence between the set { I ⊆ S : I is a strong, dense, reflexive and closed additive subsemigroup of S with I S ⊆ I } and the set of all near-ring congruences on S. We also show that in any seminearring S, there exists an inclusion preserving bijective correspondence between the set { I ⊆ S : I is a strong, dense, reflexive and closed additive subsemigroup of S with I S , S I ⊆ I } and the set of all zero-symmetric near-ring congruences on S. [ABSTRACT FROM AUTHOR]