Near-ring congruences on additively regular seminearrings. (English) Zbl 1468.16056
Summary: In this paper we first obtain analogues of some results of D. R. LaTorre [Semigroup Forum 24, 327–340 (1982; Zbl 0487.20039)] 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 S. K. Sardar and R. Mukherjee [Semigroup Forum 93, No. 3, 629–631 (2016; Zbl 1397.16046)] and Theorem 3.22 of S. K. Sardar and R. Mukherjee [Semigroup Forum 88, No. 3, 541–554 (2014; Zbl 1314.16039)] (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 [Zbl 1314.16039]. Finally we study the lattice structures of near-ring congruences and normal full \(k\)-ideals in distributively generated additively regular seminearrings.
Keywords:
additively regular seminearring; distributively generated seminearring; near-ring congruence; normal congruence; normal full right \(k\)-ideal; normal full idealReferences:
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