Overview

Original Research

SOME RESULTS ON PRIME ASSOSYMMETRIC RINGS

Dr. P. RAHIRA 1, Dr.P. SARADA DEVI 2, and Dr. S RAKMAIAH 3.

Vol 18, No 03 ( 2023 )   |  DOI: 10.17605/OSF.IO/AMZHR   |   Author Affiliation: Associate Professor, Department of Mathematics, Geethanjali College of Engineering and Technology, Chiryal, Keesara, Hyderabad, 501301, Medchel, Telangana, India 1,2; Associate Professor, Dept. of Mathematics, Vignana Bharathi Institute of Technology, Aushapur, Ghatkesar, Hyderabad, 501301, Medchal, Telangana, India 3.   |   Licensing: CC 4.0   |   Pg no: 2030-2039   |   Published on: 30-03-2023

Abstract

With the help of this paper, we want to show that 2 – and 3 – divisible Assosymmetric ring R is sub direct sum of semi prime associative ring and semi prime commutative ring also if R is a 2 – and 3 – divisible prime assosymmetric ring then R must be either Associative or Commutative. 2 – and 3 – divisible prime assosymmetric ring R is power associative, that is, (x, x, x) = 0 And Non-associative 2 – and 3 – divisible prime assosymmetric ring R satisfying the weak Novikov identity (w, x yz) = y (w, x, z), the square of every element of R is in the nucleus and then the non-zero idempotent e in R is the identity element of R.

Keywords

Assosymmetric ring, Prime ring, divisible ring, Weak Novikov identity , 2- and 3- divisible prime assosymmetric ring.