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 (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

G. Swaminathan

Ganesh Swaminathan

Department of Mathematics
Guru Nanak College
Velachery, Chennai – 600042, India

email: madmaths007@gmail.com

0000-0003-3411-8907

S. Venkatachalam

Selvan Venkatachalam

Department of Mathematics
RKM Vivekananda College
Mylapore, Chennai – 600004, India

email: venselvan@gmail.com

0000-0001-8183-3423

Title:

Derivations and semiderivations in semirings

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Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2024-07-22 , Revised: 2024-09-02 , Accepted: 2024-09-02 , Available online: 2025-06-10 , https://doi.org/10.7151/dmgaa.1482

Abstract:

In this paper, we prove that if a non-trivial derivation of a semiring commutes then the semiring is commutative. We define semiderivation in semirings and derive some of its fundamental results. We prove that a map associated with a semiderivation is always a homomorphism in an additively cancellative yoked prime semiring. We also prove that a semiderivation σ of a semiring R induces a corresponding semiderivation σΔ in RΔ, the ring of differences of the semiring R. This serves as a passage between rings and semirings and enable us to establish other conditions for commutativity of semirings with semiderivations. Our results generalizes the classical results in prime rings.

Keywords:

derivations, semiderivations, semirings and commutativity

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