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ON WEAK ARMENDARIZ RINGS

Jeon, Young-Cheol;Kim, Hong-Kee;Lee, Yang;Yoon, Jung-Sook

  • Published : 2009.01.31

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

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