On Rings With Types Of (n)-Regularity

: R . n , a R (n)- ( (n)-) b R a=abna (a=a2bn) . R (n)- ( (n)-) n , R (n)- ( (n)-) . .Let R be an associative ring with identity . For a fixed integer n >1 , an element a in R is said to be (n)-regular ( (n)-strongly regular) if there exists b in R such that a=abna (a=a2bn) . So a ring R is said to be (n)-regular ( (n)-strongly regular) for a positive integer n 1 , if every element of R is (n)-regular ( (n)-strongly regular) .In this paper we investigate some characterizations and several basic properties of those rings , also the connection between them and rings of some kind of commutivity .