Bezout Rings,Polynomials, and Distributivity

Let A be a ring, be an injective endomorphism of A, and let be the right skew polynomial ring. If all right annihilator ideals of A are ideals, then R is a right Bezout ring is a right Rickartian right Bezout ring, (e)=e for every central idempotent eA, and the element (a) is invertible in A for every regular aA. If A is strongly regular and n 2, then R/xⁿR is a right Bezout ring R/xⁿR is a right distributive ring R/xⁿR is a right invariant ring (e)=e for every central idempotent eA. The ring R/x²R is right distributive R/xⁿR is right distributive for every positive integer nA is right or left Rickartian and right distributive, (e)=e for every central idempotent eA and the (a) is invertible in A for every regular aA. If A is a ring which is a finitely generated module over its center, then A[x] is a right Bezout ring A[x]/x²A[x] is a right Bezout ring A is a regular ring.