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http://dx.doi.org/10.4134/BKMS.2009.46.1.135

ON WEAK ARMENDARIZ RINGS  

Jeon, Young-Cheol (DEPARTMENT OF MATHEMATICS KOREA SCIENCE ACADEMY)
Kim, Hong-Kee (DEPARTMENT OF MATHEMATICS AND RINS GYEONGSANG NATIONAL UNIVERSITY)
Lee, Yang (DEPARTMENT OF MATHEMATICS EDUCATION BUSAN NATIONAL UNIVERSITY)
Yoon, Jung-Sook (DEPARTMENT OF MATHEMATICS EDUCATION BUSAN NATIONAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.1, 2009 , pp. 135-146 More about this Journal
Abstract
In the present note we study the properties of weak Armendariz rings, and the connections among weak Armendariz rings, Armendariz rings, reduced rings and IFP rings. We prove that a right Ore ring R is weak Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result we can show that a semiprime right Goldie ring R is weak Armendariz if and only if R is Armendariz if and only if R is reduced if and only if R is IFP if and only if Q is a finite direct product of division rings, obtaining a simpler proof of Lee and Wong's result. In the process we construct a semiprime ring extension that is infinite dimensional, from given any semi prime ring. We next find more examples of weak Armendariz rings.
Keywords
Armendariz ring; weak Armendariz ring; reduced ring; IFP ring; classical quotient ring; semiprime ring; abelian ring; Goldie ring;
Citations & Related Records

Times Cited By Web Of Science : 5  (Related Records In Web of Science)
Times Cited By SCOPUS : 6
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