Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2009.01.31
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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

References

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