A Quick Introduction to Elliptic Curves
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چکیده
Definition 1. An element α of an extension field K of k is algebraic over k if it satisfies some monic polynomial with coefficients in k. Otherwise α is transcendental over k. A field extension K/k is algebraic if every α ∈ K is algebraic over k. A field k is algebraically closed if there is no proper algebraic extension K/k; that is, in any extension field K of k, any element α that is algebraic over k in fact lies in k. An algebraic closure k of k is a minimal algebraically closed extension field of k.
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