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Basic Abstract Algebra by S. K. Jain, S. R. Nagpaul, P. B. Bhattacharya

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CHAPTER 15

Algebraic extensions of fields

1 Irreducible polynomials and Eisenstein criterion

Let F be a field, and let F[x] be the ring of polynomials in x over F. We know that F[x] is an integral domain with unity and contains F as a proper subring. A polynomial ƒ(x) in F[x] is called irreducible if the degree of ƒ(x) 1 and, whenever ƒ(x) = g(x)h(x), where images F[x], then images F or images. If a polynomial is not irreducible, it is called reducible.

We remark ...

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