Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ANNIHILATORS IN ONE-SIDED IDEALS GENERATED BY COEFFICIENTS OF ZERO-DIVIDING POLYNOMIALS

  • Kwak, Tai Keun (Department of Mathematics Daejin University) ;
  • Lee, Dong Su (Department of Mathematics University of Ulsan) ;
  • Lee, Yang (Department of Mathematics Education Pusan National University)
  • Received : 2013.08.27
  • Published : 2014.05.01
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Abstract

Nielsen and Rege-Chhawchharia called a ring R right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, there exists a nonzero element r ${\in}$ R with f(x)r = 0. Hong et al. called a ring R strongly right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, f(x)r = 0 for some nonzero r in the right ideal of R generated by the coefficients of g(x). Subsequently, Kim et al. observed similar conditions on linear polynomials by finding nonzero r's in various kinds of one-sided ideals generated by coefficients. But almost all results obtained by Kim et al. are concerned with the case of products of linear polynomials. In this paper we examine the nonzero annihilators in the products of general polynomials.

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References

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