A note on uniquely (nil) clean ring
الموضوعات :
Sh. Sahebi
1
(Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO.
Code 14168-94351, Iran)
M. Jahandar
2
(Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO.
Code 14168-94351, Iran)
الکلمات المفتاحية: Full element, uniquely clean ring, nil clean ring,
ملخص المقالة :
A ring R is uniquely (nil) clean in case for any $a \in R$ there exists a uniquelyidempotent $e\in R$ such that $a-e$ is invertible (nilpotent). Let $C =(A VW B)$be the MoritaContext 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.