Open Access Journal

ISSN : 2456-1304 (Online)

International Journal of Engineering Research in Electronics and Communication Engineering(IJERECE)

Monthly Journal for Electronics and Communication Engineering

Open Access Journal

International Journal of Science Engineering and Management (IJSEM)

Monthly Journal for Science Engineering and Management
Call For Paper : Vol 11, Issue 03, March 2024

ISSN : 2456-1304 (Online)

Call for Paper

Vol 11, Issue 03, March 2024

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On S - Near Rings and S' - Near Rings with Right Bipotency

Author : D. Radha 1 C. Dhivya 2

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Date of Publication :13th March 2019

Abstract: A right near ring is an algebraic system with two binary operations such that (i) is a group - (not necessarily abelian) with 0 as its identity element, (ii) is a semigroup (we write for for all in ) and (iii) for all in . We say that is zero symmetric if for all in . is called an - near ring or an - near ring according as or for all . A subgroup of is called an N-subgroup if and an invariant Nsubgroup if, in addition, . An element in is said to be distributive, if for all and in ; is called distributively generated (d.g.), if the additive group of is generated by the multiplicative semigroup of distributive elements of . A near ring is defined to be right bipotent if for each in . In this paper, we have proved some more results on right bipotent near rings by using the concepts of - near ring ; subcommutativity ; regularity ; reduced property etc. It is proved that every right bipotent near ring is an - near ring and it is also - 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 and it is a division ring if it is dgnr.

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