In this paper we first obtain analogues of some results of LaTorre (Semigroup Forum 24(1):327–340, 1982) in the setting of additively regular seminearrings which in turn not only give rise to refinements of some important results viz. Propositions 3.16, 3.17, Theorem 3.20 of Sardar and Mukherjee (Semigroup Forum 93(3):629–631, 2016) and Theorem 3.22 of Sardar and Mukherjee (Semigroup Forum 88(3):541–554, 2014) (involving mainly near-ring congruences i.e., normal congruences and normal full k-ideals of additively inverse seminearrings) but also answer partially a question raised in Sardar and Mukherjee (Semigroup Forum 88(3):541–554, 2014). Finally we study the lattice structures of near-ring congruences and normal full k-ideals in distributively generated additively regular seminearrings.

中文翻译：

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附加规则研讨会上的近环同余

在本文中，我们首先获得了 LaTorre (Semigroup Forum 24(1):327–340, 1982) 在附加规则研讨会的设置中的一些结果的类似物，这反过来不仅导致了一些重要结果的改进，即。命题 3.16、3.17、Sardar 和 Mukherjee 的定理 3.20（Semigroup Forum 93(3):629–631, 2016）和 Sardar 和 Mukherjee 的定理 3.22（Semigroup Forum 88(3):541–554，主要涉及近 2222 -环同余，即加法逆半环的正余同余和正态全 k-理想），但也部分回答了 Sardar 和 Mukherjee 提出的问题（半群论坛 88(3):541–554, 2014）。最后，我们研究了分布生成的加法规则研讨会中近环同余和正常全 k 理想的晶格结构。