A note on uniquely (nil) clean ring

محورهای موضوعی : History and biography

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)

تاریخ دریافت : 1390/10/11 تاریخ پذیرش : 1391/01/13 تاریخ انتشار : 1391/03/12

کلید واژه: Full element, uniquely clean ring, nil clean ring,

چکیده مقاله :

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.

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