Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON COEFFICIENTS OF NILPOTENT POLYNOMIALS IN SKEW POLYNOMIAL RINGS

  • Nam, Sang Bok (Department of Early Child Education Kyungdong University) ;
  • Ryu, Sung Ju (Department of Mathematics Pusan National University) ;
  • Yun, Sang Jo (Department of Mathematics Pusan National University)
  • Received : 2013.10.18
  • Accepted : 2013.11.25
  • Published : 2013.12.30
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Abstract

We observe the basic structure of the products of coefficients of nilpotent (left) polynomials in skew polynomial rings. This study consists of a process to extend a well-known result for semi-Armendariz rings. We introduce the concept of ${\alpha}$-skew n-semi-Armendariz ring, where ${\alpha}$ is a ring endomorphism. We prove that a ring R is ${\alpha}$-rigid if and only if the n by n upper triangular matrix ring over R is $\bar{\alpha}$-skew n-semi-Armendariz. This result are applicable to several known results.

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References

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