Date

2024-6

Type

Article

Journal title

جامعة طرابلس

Issue

Vol. 0 No. 31

Author(s)

Abir Khalil Salibi

Pages

47 - 67

Abstract

In this work, the concept of Smarandache idempotent element introduced as a generalization of the idempotent element in Z_n, (the ring of integers modulo n). In a previous research paper[5], we found the idempotent elements in Z_n ,(n=2pq) where p,q are different odd primes, in this paper we introduced another idempotent in Z_n . We describe n such that every non-trivial idempotent in Z_n is S-idempotent and we have shown the existence of Smarandache idempotents (S-idempotents) in the ring Z_n when n=2p,pq,2pq,pqr , and in general when n = p_1^(α_1 ) p_2^(α_2 )⋯p_m^(α_m ) and obtain their numbers, we illustrate them with several examples.