On Generalized - Regular Rings

. :1. R R .2. R l(an) r(an), a R n R R . The purpose of this paper is to study right generalized -regular rings and give some of it is properties. Also, we proved: 1- Let R be a right generalized -regular ring without zero divisors element. Then R is a division ring.2- 2- Let R be a ring with l(an) r(an), for every a R and n . Then R is regular. If and only if R is a right generalized -regular ring.