We continue the study of a zip ring under a weaker condition of annihilators and call it a generalized zip ring. Of course, every zip ring is a generalized zip ring, but by means of an example, it is shown that a generalized zip ring may not be a zip ring. Also, every (quasi-) Baer ring with identity is a generalized zip ring. We obtain some properties of a generalized zip ring and examine various kinds of basic extensions of a generalized right zip. We show that a generalized right zip ring may become a polynomial ring, a Laurent polynomial ring or an n by n full matrix ring.

zip ring, polynomial ring, Laurent polynomial ring, matrix ring.