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On generalized derivations of semirings

  • Madhu Dadhwal EMAIL logo and Geeta Devi

Abstract

In this paper, the notion of generalized derivations is characterized. Also, the action of these derivations on ideals is investigated and as a consequence, some results involving commutator identities are proved. Further, we explore the commutativity of prime additively inverse semirings in which generalized derivations satisfy certain differential identities. An extension to Posner’s second theorem is also established in the framework of generalized derivations.

MSC 2010: 16Y60; 16N60

Funding statement: The second author also gratefully acknowledges the financial assistance she received from U.G.C., India.

Acknowledgements

The authors are very grateful to the referees for their careful reading of the manuscript and many valuable suggestions.

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Received: 2021-11-14
Revised: 2022-02-25
Accepted: 2022-03-16
Published Online: 2022-07-22
Published in Print: 2022-10-01

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