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Classification and prime decomposition of abelian q-fields 被引量:1

Classification and prime decomposition of abelian q-fields
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摘要 Let q be any rational prime number.An abelian q-field L is a Galois extension overQ with Galois group as an abelian q-group(i.e.an abelian group whose order is a powerof q).We here will give the classification of all the abelian q-fields L,the explicit law ofprime decomposition of any prime number p in L,the inertia groups,residue class de-grees,and discriminants of L,developing systematically and completely the results onfields of types(2,2,…,2),(q, q,…,q),and(q^s,q^s,…,q^s)in many references obtainedby specific method in each case.
作者 张贤科
出处 《Chinese Science Bulletin》 SCIE EI CAS 1996年第24期2025-2028,共4页
基金 Project supported by the National Natural Science Foundation of China.
关键词 number FIELD ABELIAN FIELD pnme DECOMPOSITION CLASSIFICATION factorization. number field Abelian field prime decomposition classification factorization
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同被引文献13

  • 1Zhang Xianke.The relative integral bases and unit of the number fields of type (l ,l , …,l ). Acta Mathematica Sinica . 1986
  • 2Zhang Xianke.On number fields of type (2,2,…,2) , J.China Univ. Science and Technology . 1982
  • 3Zhang Xianke.Existence of integral basis for relative extensions of n-cyclic number fields, J. Journal of Number Theory . 1996
  • 4MacKenzie R,Scheuneman J.A number field without a relative integral basis. The American Mathematical Monthly . 1971
  • 5Bird R,Parry C J.Integral bases for bicyclic biquadratic fields over quadratic subfields. Pacific Journal of Mathematics . 1976
  • 6Washington,L. C.Relative integral bases, Proc. Journal of the American Mathematical Society . 1976
  • 7Fujisaki G.Some examples of number fields without relative integral bases. J Fac Sci Univ Tokyo, Sect IA . 1974
  • 8Zhang Xianke.Cyclic quartic fields and genus theory of their subfields, J. Journal of Number Theory . 1984
  • 9Zhang Xianke.Relative integral bases of cyclic quartic number fields, Acta Math. Sinica . 1984
  • 10Zhang Xianke.A simple construction of genus fields of abalian number fields, Proc. Journal of the American Mathematical Society . 1985

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