SOME REMARKS ON EISENSTEIN'S CRITERION Woo, Sung-Sik;
In  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.
irreducibile polynomial over a commutative ring;
Bourbaki, Elements of Mathematics, Algebra II, Addison-Wesley, 1973
Bourbaki, Elements of Mathematics, Commutative Algebra, Addison-Wesley, 1972
D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, New York Berlin, 1995
S. S. Woo, Dividing polynomials using the resultant matrix, Comm. Alg. 35 (2007), 3263- 3272