Research ArticleNo Access

Commutativity in 3-prime nearrings through permutation identities

S. Aishwarya

Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Karnataka, India

E-mail Address: aishwarya93s@gmail.com

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Kedukodi Babushri Srinivas

Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Karnataka, India

E-mail Address: babushrisrinivas.k@manipal.edu

Corresponding author.

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, and

Kuncham Syam Prasad

Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Karnataka, India

E-mail Address: syamprasad.k@manipal.edu

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https://doi.org/10.1142/S1793557122501091Cited by:4 (Source: Crossref)

Abstract

In this paper, we investigate permutation identities satisfied by semigroup left ideals and weak semigroup left ideals in prime nearrings. We obtain results on commutativity of multiplication and addition using these identities. We provide examples to show the necessity of certain conditions in some of the results obtained. Finally, we give a characterization of Galois field in terms of permutation identities.

Communicated by A. R. Rajan

Keywords:

AMSC: 16Y30, 16N60, 16U80

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