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QUASI-ARMENDARIZ PROPERTY FOR SKEW POLYNOMIAL RINGS

Baser, Muhittin;Kwa, Tai Keun

  • Received : 2010.07.19
  • Published : 2011.10.31

Abstract

The concept of the quasi-Armendariz property of rings properly contains Armendariz rings and semiprime rings. In this paper, we extend the quasi-Armendariz property for a polynomial ring to the skew polynomial ring, hence we call such ring a ${\sigma}$-quasi-Armendariz ring for a ring endomorphism ${\sigma}$, and investigate its structures, several extensions and related properties. In particular, we study the semiprimeness and the quasi-Armendariz property between a ring R and the skew polynomial ring R[x;${\sigma}$$] of R, and so these provide us with an opportunity to study quasi-Armendariz rings and semiprime rings in a general setting, and several known results follow as consequences of our results.

Keywords

quasi-Armendariz property;skew polynomial ring;semiprime ring;rigid ring

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