• TAI KEUN KWAK

      Articles written in Proceedings – Mathematical Sciences

    • Structure of weakly one-sided duo Ore extensions

      CHAN YONG HONG HONG KEE KIM NAM KYUN KIM TAI KEUN KWAK YANG LEE YANG LEE

      More Details Abstract Fulltext PDF

      Marks (J. Algebra 280 (2004) 463–471) proved that if the skew polynomial ring $R[x; \sigma]$ is left or right duo, then $R[x; \sigma]$ is commutative. It is proved that if $R[x; \sigma]$ is weakly left (resp., right) duo over a reduced ring $R$ with an endomorphism (resp., a monomorphism) $\sigma$, then $R[x; \sigma]$ is commutative. This concludes that a noncommutative skew polynomial ring is not weakly left duo when the base ring is reduced. It is also shown that if $R[x; \sigma]$ is weakly left duo then the polynomial ring $R[x]$ is weakly left duo. We next study the structure of the Ore extension $R[x; \sigma, \delta]$ when it is weakly left or right duo.

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