Near-ring congruences on additively regular seminearrings

Autor:	Sujit Kumar Sardar, Pavel Pal, Kamalika Chakraborty
Rok vydání:	2020
Předmět:	Near-ring Pure mathematics Algebra and Number Theory 010201 computation theory & mathematics Semigroup 010102 general mathematics Inverse 0102 computer and information sciences 0101 mathematics Algebra over a field Congruence relation 01 natural sciences Mathematics
Zdroj:	Semigroup Forum. 101:285-302
ISSN:	1432-2137 0037-1912
DOI:	10.1007/s00233-020-10123-4
Popis:	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.
Databáze:	OpenAIRE
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