Abstract:

An endomorphism α of a ring R is called right reversible if whenever ab=0  for a,b∈R,bα(a)=0. A ring R is called right α-reversible if there exists a right reversible endomorphism α of R. The relations between α-reversible, α-rigid, reversible and weak α-skew Armendariz rings are investigated. And it is proven that for reversible and right α-reversible rings R: (1) R is a weak α-skew Armendariz ring; (2) R［x］／(xⁿ) is a weak α-skew Armendariz ring for any positive integer n; (3) If for some positive integer t, α^t=1_R, then R［x;α］ is weak Armendarizring.
 

Key words: α-reversible ring; α-rigid ring; weak α-skew Armendariz ring