Eisenstein's criterion

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Related lectures (32)

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Algebraic Extensions

Explores algebraic extensions, constructions, irreducible polynomials, autonomous constructions, and cutting compositions.

Integration of Simple Elements

Covers the integration of simple elements and limit expansions with examples.

The Ring of Eisenstein Integers: Properties and Applications

Covers the properties of the ring of Eisenstein integers and its submodule structure.

Integration on H_pxH and Arithmetic

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Decimal Expansion: Division and Periodicity

Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Polynomial Factorization: Field Approach

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

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Polynomial Factorization and Decomposition

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.