• Title/Summary/Keyword: Ore quotient rings

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THE COHN-JORDAN EXTENSION AND SKEW MONOID RINGS OVER A QUASI-BAER RING

  • HASHEMI EBRAHIM
    • Communications of the Korean Mathematical Society
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    • v.21 no.1
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    • pp.1-9
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    • 2006
  • A ring R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. Let R be a ring, G be an ordered monoid acting on R by $\beta$ and R be G-compatible. It is shown that R is (left principally) quasi-Baer if and only if skew monoid ring $R_{\beta}[G]$ is (left principally) quasi-Baer. If G is an abelian monoid, then R is (left principally) quasi-Baer if and only if the Cohn-Jordan extension $A(R,\;\beta)$ is (left principally) quasi-Baer if and only if left Ore quotient ring $G^{-1}R_{\beta}[G]$ is (left principally) quasi-Baer.

ON WEAK ARMENDARIZ RINGS

  • Jeon, Young-Cheol;Kim, Hong-Kee;Lee, Yang;Yoon, Jung-Sook
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.1
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    • pp.135-146
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    • 2009
  • 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.