DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

V . Selvan

Venkatachalam Selvan

Associate Professor
Department of Mathematics
RKM Vivekananda College
Chennai - 600004, India

email: venselvan@gmail.com

http://orcid.org/0000-0001-8183-3423

S. Ganesh

Swaminathan Ganesh

Research Scholar
Department of Mathematics
RKM Vivekananda College
Chennai - 600004, India

email: madmaths007@gmail.com

0000-0003-3411-8907

Title:

Reverse derivations and generalized reverse derivations in semirings

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Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2022-11-22 , Revised: 2023-01-15 , Accepted: 2023-01-22 , Available online: 2023-07-12 , https://doi.org/10.7151/dmgaa.1439

Abstract:

In this article we extend the results on reverse derivation in rings to semirings. First we dispose of reverse derivations in prime semirings analogous to Herstein's result [7]. Then, we prove that reverse derivation is just an ordinary derivation in semiprime semirings if and only if it is a central derivation. We also define generalized reverse derivations and obtain some commutativity results which extend the results in [11]. The primary technique we use in these results is the use of derivations and reverse derivations in ring of differences $R^\Delta$ corresponding to the semiring $R$ and the fact that $R$ is embedded in $R^\Delta$. This fact allows us to travel back and forth between $R$ and $R^\Delta$ and serve as a key tool in obtaining the desired results.

Keywords:

Reverse derivations, derivations, semirings, l-generalized reverse derivations, r-generalized reverse derivations, generalized reverse derivations, and semiprime semirings

References:

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