According to Wedderburn's little theorem, every finite domain is a finite one of these and therefore has prime power order. An extension is said to be
According to Wedderburn's little theorem, every finite domain is a finite one of these and therefore has prime power order. An extension is said to be "Galois" if the one of these fixed by the automorphism group of the extension is the base one of these. Given a polynomial, "splitting" ones of these are defined to be extensions for which the polynomial can be completely factored into linear factors. The quotient of a ring with one of its maximal ideals is one of these entities. These entities have no nontrivial ideals, and the only finite ones are of order p to the k, where p is prime. Given an integral domain, it is always possible to form one of these from its fractions. For 10 points, name this algebraic structure which has two binary operations and inverses for both, examples of which include the complex numbers, the real numbers, and the rational numbers.
According to Wedderburn's little theorem, every finite domain is a finite one of these and therefore has prime power order.
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