Rings in Which Every Element is Sum of a Unit and Finitely Many Nonzero Idempotents

Abstract

We define a ring R to be a UI - ring when each element of R can be represented as the sum
of a unit and finitely many nonzero idempotents of R. In this article we have shown that semisimple rings,
artinian rings and semiprimary rings are UI - ring. Also we have proved if R is a UI - ring then for every
n > 1, Mn(R) is a UI - ring and for each n > 1, R is a UI - ring if and only if Tn(R) is a UI - ring.