Relative integral bases of abelian q-fields 被引量：1

Relative integral bases of abelian q-fields

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摘要 Let O_L and O_K denote the rings of integers in the algebraic number fields L and K, respectively, where K is a subfield of L. If O_L is a free O_K-module, then L/K is said to have a relative integral basis. Artin and Frhlich raised and studied the problem of existence of a relative integral basis for a number field L. The nroblem was treated

作者张贤科

机构地区 Department of Mathematics

出处《Chinese Science Bulletin》 SCIE EI CAS 1996年第13期1065-1068,共4页

基金 Project supported by the National Natural Science Foundation of China.

关键词 number FIELD ABELIAN FIELD RELATIVE INTEGRAL basis CHARACTER group. number field Abelian field relative integral basis character group

分类号 O172.2 [理学—基础数学]

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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

引证文献1

1张贤科.Structure and prime decomposition law and relative extensions of abelian fields with prime power degree[J].Science China Mathematics,1999,42(8):816-824.

1张贤科.NOTE ON A PAPER BY A.A.ALBERT[J].Chinese Science Bulletin,1984,29(11):1434-1435.
2冯克勤,张贤科.ON RELATIVE INTEGRAL BASES OF QUARTIC CYCLIC NUMBER FIELDS[J].Chinese Science Bulletin,1983,28(4):456-457.
3刘通.Congruences for the class numbers of real cyclic sextic number fields[J].Science China Mathematics,1999,42(10):1009-1018. 被引量：2
4王元.ON ADDITIVE EQUATIONS IN AN ALGEBRAIC NUMBER FIELD[J].Chinese Science Bulletin,1985,30(5):583-587.
5王世强.GOLDBACH AND NON-GOLDBACH EXTENSIONS OF SOME CYCLO-TOMIC RINGS OF INTEGERS[J].Chinese Science Bulletin,1985,30(5).
6冯克勤.ARITHMETIC CHARACTERI ZATION OF ALGEBRAIC NUMBER FIELDS WITH GIVEN CLASS GROUP[J].Chinese Science Bulletin,1984,29(3):419-420.
7王元.ON A SYSTEM OF DIOPHANTINE INEQUALITIES[J].Chinese Science Bulletin,1987,32(17):1162-1165.
8张贤科.Structure and prime decomposition law and relative extensions of abelian fields with prime power degree[J].Science China Mathematics,1999,42(8):816-824.
9YANG Min,MENG QingShu,WANG ZhangYi,LI Li,ZHANG HuanGuo.On the coefficients of the polynomial in the number field sieve[J].Science China(Information Sciences),2015,58(11):178-186.
10Xue Jun GUO,Guang Tian SONG Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China.A Remark on Computing the Tame Kernel of Quadratic Imaginary Fields[J].Acta Mathematica Sinica,English Series,2002,18(3):513-516.

Chinese Science Bulletin

1996年第13期

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Relative integral bases of abelian q-fields 被引量：1

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