ON QUASI PRIME PERIODIC RINGS

Abstract: A ring R will be called Quasi-Periodic if for each x ∈ R, there exist integers k, n, m all depending on x, such that n > m > 0 and xn = kxm . The concepts of Quasi Periodic Rings are introduced by Howard E.Bell. Now we restrict the condition for k from any integer to a prime number. We define a quasi prime periodic ring as A ring R such that for each x ∈ R, there exist integers n, m and any prime number k all depending on x, such that n > m > 0 and xn = kxm. Then we compare these quasi prime periodic rings with quasi periodic rings. We give the proof of direct sum of quasi prime periodic rings and nil rings is a quasi prime periodic ring and homomorphic image of a quasi prime periodic ring is a homomorphic ring. Then we study under what conditions quasi prime periodic rings are reduced.