Study of Additively Regular Г -Semirings and Derivations

Discussiones Mathematicae - General Algebra and Applications

Neelam¹  Dadhwal Madhu¹ 

[1] Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India;

关键词: semirings;    г -semirings;    additively regular г -semirings;    derivations and commutators;    16y60;    16y99;   

DOI  :  10.7151/dmgaa.1378

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown