• D.Radha
• C.Dhivya
• M.Vinutha
• K.Muthu Maheswari
• S.R.Veronica Valli

In this paper we introduce the concept of R-near ring. We define that a near ring N is a R-near ring if for every a in N, there exists x in N such that xax=xa. The properties of R-near ring are discussed using the concept of zero divisors, ideal and subcommutativity. It is proved that every ideal and every left N-subgroup of any R-near ring without zero divisors is an R-near ring. It is also proved that any R-near ring is IFP near ring and subcommutative if it is Boolean; zero-symmetric if it is commutative also. A commutative zero symmetric Boolean near ring is always a R-near ring.

N-subgroup, IFP, subcommutative, nil near ring, distributive, Boolean

"A Study on R-Near Ring", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 12, page no.434-439, December-2019, Available :http://www.jetir.org/papers/JETIR1912055.pdf

"A Study on R-Near Ring", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 12, page no. pp434-439, December-2019, Available at : http://www.jetir.org/papers/JETIR1912055.pdf