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SOME REMARKS ON THE PRIMARY IDEALS OF ℤpm[X]

  • Woo, Sung-Sik (Department of Mathematics Ewha Women's University)
  • Published : 2006.10.31

Abstract

In [2], they found some natural generators for the ideals of the finite ring $Z_{pm}$[X]/$(X^n\;-\;1)$, where p and n are relatively prime. If p and n are not relatively prime $X^n\;-\;1$ is not a product of basic irreducible polynomials but a product of primary polynomials. Due to this fact, to consider the ideals of $Z_{pm}$[X]/$(X^n\;-\;1)$ in 'inseparable' case we need to look at the primary ideals of $Z_{pm}$[X]. In this paper, we find a set of generators of ideals of $Z_{pm}$[X]/(f) for some primary polynomials f of $Z_{pm}$[X].

Keywords

References

  1. M. Atiyah, Addison-Wesley (1965)
  2. P. Kanwar and Sergio, Cyclic codes over integer modulo $p^n$, finite fields and their applications 3(2) (1997)
  3. S. Lang, Algebra, 3rd ed., Addison Wesley, 1993
  4. B. R. McDonalds, Finite rings with identity, Dekker, New York, 1974