Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOME REMARKS ON EISENSTEIN'S CRITERION

  • Woo, Sung-Sik (DEPARTMENT OF MATHEMATICS EWHA WOMEN'S UNIVERSITY)
  • Published : 2008.10.31
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Abstract

In [4] we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coefficients of the polynomials which we called the resultant matrix. Using the result, we will find conditions for a polynomial over a commutative ring to be irreducible. This can be viewed as a generalization of the Eisenstein's irreducibility criterion.

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References

  1. Bourbaki, Elements of Mathematics, Algebra II, Addison-Wesley, 1973
  2. Bourbaki, Elements of Mathematics, Commutative Algebra, Addison-Wesley, 1972
  3. D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, New York Berlin, 1995
  4. S. S. Woo, Dividing polynomials using the resultant matrix, Comm. Alg. 35 (2007), 3263- 3272 https://doi.org/10.1080/00927870701658185