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Elsevier B.V.
DOI: 10.1016/s0079-8169(08)62291-6
  • Mathematics


Publisher Summary This chapter discusses the information on the algebraic number. A finite algebraic number field K is a finite extension of the rational number field k = Q; a finite algebraic function field K is a finite extension of the rational function field k = ko(xl, …, xm,) in the m variables xi over some field of constants ko. The chapter also discusses the number and function fields, thus take for granted the prefix “finite algebraic,” but sometimes distinguishes between “algebraic” and “rational.” There is a remarkable similarity between algebraic number and function fields that permits a common treatment of both, and manifested in the formal analogy between the integral domains i = Z of rational integers and i = ko[x] of rational functions. Both are Euclidean domains.

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