Commutative Medial Near Ring

Dhivya C, Radha D


We deliberate a substructure of a near ring called mediality so as to create a new platform, on which many of the properties like commutativity, regular, idempotent and zero symmetric are applied with. It is shown that every medial near ring is commutative whenever cancellation law holds. Commutative medial near ring is left medial, right medial, reverse, reverse medial, reverse left medial and reverse right medial. It is proved that a non-trivial left medial regular near ring is reduced. Also, a structure theorem has been obtained.


Commutative; Medial; Nilpotent; Regular; Zero symmetric

Full Text:



Fitore Abdullahu and Abdullah Zejnullahu. Notes on semimedial semigroups. Commentationes Mathematicae Universitatis Carolinae, 50(3):321–324, 2009.

Muhammad Akram, Naveed Yaqoob, and Madad Khan. On (m, n)-ideals in la-semigroups. Applied Mathematical Sciences, 7(44):2187–2191, 2013.

Akin Osman Atagun, Huseyin Kamaci, Ismail Tastekin, and Aslihan Sezgin. P-properties in near-rings. 2019.

R Balakrishnan and S Suryanarayanan. On pk and pk’ near-rings. Bulletin of the Malaysian Mathematical Sciences Society, 23(1):9–24, 2000.

R Balakrishnan and S Suryanarayanan. P (r, m) near-rings. Bulletin of the Malaysian Mathematical Sciences Society, 23(2), 2000.

Gary Birkenmeier and Henry Heatherly. Medial near-rings. Monatshefte für Mathematik, 107:89–110, 1989.

JL Jat and SC Choudhary. On left bipotent near-rings. Proceedings of the Edinburgh Mathematical society, 22(2):99–107, 1979.

Silvia Pellegrini Manara. On medial near-rings. In North-Holland Mathematics Studies, volume 137, pages 199–209. Elsevier, 1987.

Attila Nagy and Attila Nagy. Right commutative semigroups. Special Classes of Semigroups, pages 137–173, 2001.

R Perumal and P Chinnaraj. Medial left bipotent seminear-rings. In Mathematics and Computing: ICMC, Haldia, India, January 2015, pages 451–457. Springer, 2015.

Gunter Pilz. Near-rings: the theory and its applications. Elsevier, 2011.

Syed Aleem Shah, Aleem Syed, and Nisar Shah. Study some new relations of medial and paramedial magmas with semigroups, la (ra) and ldd (rdd) semigroups. 2020.

S Uma, R Balakrishnan, and T Tamizh Chelvam. Pseudo commutative near-rings. Department of Mathematics Northwest University, 6(2):75–85, 2010.



  • There are currently no refbacks.

Copyright (c) 2023 Dhivya C, Radha D

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.