Commutative Medial Near Ring

Authors

  • Dhivya C A.P.C.Mahalaxmi College for Women, Thoothukudi - 628003, Tamilnadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti Tirunelveli – 627012, Tamilnadu, India
  • Radha D A.P.C.Mahalaxmi College for Women, Thoothukudi - 628003, Tamilnadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti Tirunelveli – 627012, Tamilnadu, India

DOI:

https://doi.org/10.23755/rm.v48i0.1193

Keywords:

Commutative, Medial, Nilpotent, Regular, Zero symmetric

Abstract

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.

References

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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