Field Theory

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5 domain-specific abstractions whose origin domain is Field Theory.

• Degree of a field extension — The vector-space dimension of an extension field over its base field.
• Minimal polynomial (field theory) — The unique monic polynomial of least positive degree over a base field having a given algebraic extension element as a root.
• Quasi-algebraically closed field — Classify a field as C1 when every nonconstant homogeneous form of degree d in more than d variables has a nontrivial zero over that field.
• Rupture field — A field extension generated by adjoining one root of a polynomial over the base field.
• Separable polynomial — A polynomial over a field whose roots in an algebraic closure are all distinct.