| 31. | :: : : Any algebraic number has an associated base in which all integers terminate.
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| 32. | Dedekind's first contribution concerns the theorem that the set of real algebraic numbers is countable.
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| 33. | Ramification in algebraic number theory means prime numbers factoring into some repeated prime ideal factors.
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| 34. | An example of an active area of research in algebraic number theory is Iwasawa theory.
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| 35. | For a given algebraic number ? and algebraic number field " K ", the equation
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| 36. | Their detailed properties are studied in algebraic number theory.
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| 37. | It is of particular interest for local fields and global fields, such as algebraic number fields.
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| 38. | By applying his construction to the sequence of real algebraic numbers, Cantor produces a transcendental number.
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| 39. | The periods are intended to bridge the gap between the algebraic numbers and the transcendental numbers.
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| 40. | Examples come from fractional ideals in algebraic number theory, so that the definition captures that theory.
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