algebraic number field


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algebraic number field

[¦al·jə¦brā·ik ′nəm·bər ‚fēld]
(mathematics)
A finite extension field of the field of rational numbers.
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References in periodicals archive ?
In this paper, we study the remaining parts, namely, we give such bounds for modular forms with Fourier coefficients in an arbitrary algebraic number field K and for any prime ideal p in K.
i) The usual definition is more general, the coefficients of S can be taken in an arbitrary algebraic number field.
Let p be an odd prime and k an algebraic number field of finite degree such that the p-rank of Cl(k) is equal to 2.
presents an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization.
of Tokyo) explore similarities between algebraic number fields and algebraic function fields in one variable over finite fields, explain adele rings and idele groups, derive several prime number theorems, and prove the main theorem of class field theory.
Stan, Florin, University of Illinois, Urbana-Champaign, Trace problems in algebraic number fields and applications to characters of finite groups.

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