Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 210


In this paper, with the useful resource of defining P- $\pi$ regular near-ring, we make a new method of $\pi$ regular of order two in the near ring. Every P- $\pi$ regular is a strongly P- $\pi$ regular and additionally strongly P- $\pi$ regular is a weakly P- $\pi$ regular all are equivalent. And discussed some of the results. Every regular near ring is a $\pi$ regular ring and $\pi$ regular is a regular near-ring. Previously, we introduce the conception of strongly P-regular Near rings [9]. We have displayed that a Near ring N is strongly P-regular if and only if it is also regular. A Near-ring N is called left(right) strongly P-regular if for every 'a' there is an 'n’ in N such that $a=na^{2}+p ~~(a=a^{2} n+p)$ and $a=ana$, position P is an arbitrary ideal. We specify some new concepts and justify them with suitable examples. And also, we discuss some of the theorems related to it.

Keywords and Phrases

Near-ring[NR], $\pi$ regular, P-$\pi$ regular, $\pi$-regular of order 2.

A.M.S. subject classification

16Y30, 12K05.


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