• D.Radha
• C.Dhivya

A right near ring (N,+,⋅) is an algebraic system with two binary operations such that (i) (N,+) is a group - (not necessarily abelian) with 0 as its identity element, (ii) (N,⋅) is a semigroup (we write xy for x⋅y for all x,y in N) and (iii) (x+y)z=xz+yz for all x,y,z in N. We say that N is zero symmetric if n0=0 for all n in N. N is called an S - near ring or an S' - near ring according as x∈Nx or x∈xN for all x∈N. A subgroup M of N is called an N-subgroup if NM⊂M and an invariant N-subgroup if, in addition, MN⊂M. An element a in N is said to be distributive, if a(b+c)=ab+ac for all b and c in N; N is called distributively generated (d.g.), if the additive group of N is generated by the multiplicative semigroup of distributive elements of N. A near ring N is defined to be right bipotent if aN=a^2 N for each a in N. In this paper, we have proved some more results on right bipotent near rings by using the concepts of S' - near ring ; subcommutativity ; regularity ; reduced property etc. It is proved that every right bipotent near ring is an S' - near ring and it is also S - near ring if it is also subcommutative. Every regular near ring is central and reduced if it is right bipotent. Some special characterizations are obtained in such a way that, a reduced right bipotent near ring is a near field if N = N_d and it is a division ring if it is dgnr.

S near ring, S^'- near ring, near field, right bipotent near ring, subcommutative, nilpotent, right N - subgroup, zero divisors, regular near ring, division ring, distributively generated near ring

"On S - Near Rings and S' - Near Rings with Right Bipotency", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 2, page no.995-1000, February-2019, Available :http://www.jetir.org/papers/JETIRAB06186.pdf

"On S - Near Rings and S' - Near Rings with Right Bipotency", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 2, page no. pp995-1000, February-2019, Available at : http://www.jetir.org/papers/JETIRAB06186.pdf