A SHORT NOTE ON IDEMPOTENT RINGS

Abstract

In this paper we introduce a new class of rings that we say idempotent rings.  We call a ring R is idempotent, if every ideal of R is generated by an idempotent element.  In this paper we prove some properties of this rings, where one of the important results is the following:
     Let t ≥ 2 be an integer number.  Then the ring \(\mathbb{Z}_t\) is an idempotent ring if and only if t= p₁p₂ . . . p_n, where all of the p_i are distinct prime numbers.