Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran
A ring R is uniquely (nil) clean in case for any a 2 R there exists a uniquely
idempotent e 2 R such that a e is invertible (nilpotent). Let C =
be the Morita
Context ring. We determine conditions under which the rings A;B are uniquely (nil) clean.
Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.