1) Galois extension
Galois扩张
1.
According to the Galois extension theory of the number field,the discriminant of the field and the integral basis theory,the necessary and sufficient condition is attained which is m≡n≡1(mod4),where m and n are two different rational integers without square factors.
四次域是重要的Galois数域之一,该文对四次域Q(m,n)进行了讨论;利用Galois扩张、域的判别式及整基等一些理论,得出了其具有正规整基的充要条件为m≡n≡1(mod4)(其中m,n是2个不同的无平方因子有理整数)。
2) weak galois extension
弱Galois扩张
1.
Then weak Galois extension is introduced and it gives a sufficient condition to infer weak Galois extension .
然后介绍了弱Hopf代数上的弱Galois扩张,并给出了判定弱Galois扩张的一个充分条件。
3) Galois coextension
Galois余扩张
1.
Let H be a finite dimensional Hopf algebra, C a right H -module coalgebra and R=C/CH + Suppose that C/R is an H -Galois coextension,and both R and R H * satisfy Krull-Schmidt property for injective comodules.
如果C/R是M Galois余扩张且R及R H 关于内射余模满足Krull schmidt性质 ,我们证明了C是交叉余积的主要条件是CR 为自由余模。
4) Hopf Galois extensions
Hopf-Galois扩张
5) p adic number field
Galois-根扩张
6) Hopf-bi-Galois extension
Hopf-双Galois扩张
1.
This paper is devoted totwo aspects: one is the smash product of a semisimple Hopf algebra and its transitivemodule algebra which has a 1-dimensional ideal; the other is faithfully flat Hopf-bi-Galois extensions.
本文主要研究两方面的内容:一方面为半单Hopf代数与其可迁模代数的smash积的结构;另一方面为忠实平坦的Hopf-双Galois扩张。
补充资料：Galois扩张
Galois扩张
Galois extension
〔加如台扩张【C汕血巴恤d团;T助ya pae山.peo.e」，域的 正规并且可分的域的代数扩张(见域的扩张(exten.sion of a field)).这种扩张的自同构群的研究构成了Ca如如理论(Calois tl贺幻ry)的一部分. 裴定一译赵春来校
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参考词条