Study of Additively Regular Г -Semirings and Derivations

Abstract

In this paper, the notions of commutator and derivation in additively regular -semirings with (A2, Г)-condition are introduced. We also characterize Jordan product for additively regular Г -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
• г -semirings
• additively regular г -semirings
• derivations and commutators
• 16y60
• 16y99