JP Journal of Algebra, Number Theory and Applications
Volume 48, Issue 2, Pages 177 - 192
(November 2020) http://dx.doi.org/10.17654/NT048020177 |
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ON GENERALIZED ZIP RINGS
Jeong Sook Park and Kye Hee Park
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Abstract: 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. |
Keywords and phrases: zip ring, polynomial ring, Laurent polynomial ring, matrix ring.
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