Some remarks on Eisenstein's criterion
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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.
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.
참고문헌 (4)
- Bourbaki, "Elements of Mathematics, Algebra II" (1973), Addison-Wesley
- Bourbaki, "Elements of Mathematics, Commutative Algebra" (1972), Addison-Wesley
- D. Eisenbud, "Commutative Algebra with a View Toward Algebraic Geometry" (1995), Springer-Verlag
- S. S. Woo, "Dividing polynomials using the resultant matrix", Comm. Alg, 35, pp.3263~3272 (2007)