Geodesic
Study of Additively Regular Г-Semirings and Derivations
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 201-215

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In this paper, the notions of commutator and derivation in additively regular Г-semirings with (A2, Г)-condition are introduced. We also characterize Jordan product for additively regular -semiring and establish some results which investigate the relationship between commutators, derivations and inner derivations. In 1957, E.C. Posner has shown that if there exists a non-zero centralizing derivation in a prime ring R, then R is commutative. This result is extended in the frame work of derivations of prime additively regular Г-semirings.
Keywords: semirings, derivations and commutators, Г-semirings, additively regular Г-semirings 
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Dadhwal, Madhu; Neelam. Study of Additively Regular Г-Semirings and Derivations. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 201-215. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_1_a9/