| 21. | Many classic examples of this stem from algebraic number theory.
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| 22. | The algebraic numbers form a subfield of the real numbers.
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| 23. | In addition, they can also be closely approximated by algebraic numbers of degree 4,
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| 24. | It covers elementary and algebraic number theory, including Dirichlet's theorem.
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| 25. | Thirdly, groups were, at first implicitly and later explicitly, used in algebraic number theory.
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| 26. | His mathematical work was in algebraic number theory and abstract algebra, especially group theory.
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| 27. | All roots of polynomials with rational coefficients are algebraic numbers, by definition of the latter.
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| 28. | He introduced the Tamagawa numbers, which are measures for algebraic groups over algebraic number fields.
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| 29. | One of the origins of the mathematical theory of arithmetic groups is algebraic number theory.
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| 30. | For a given algebraic number ? and algebraic number field " K ", the equation
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