Credence
发表于 2025-3-26 21:33:28
Introduction,Once the framework of Galois theory has been completed with the main theorem, the principal problem of the theory is the question: what are the possible normal extensions of a fixed base field . with given Galois group .. This problem is called the ..
senile-dementia
发表于 2025-3-27 04:20:54
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crescendo
发表于 2025-3-27 08:54:08
Galois Theory of Infinite Algebraic Extensions,A Galois theory of a category R is a contravariant functor of R into a “simpler” category R′, where certain properties of the objects and morphisms of R are reflected in R′.
Enzyme
发表于 2025-3-27 11:38:38
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angina-pectoris
发表于 2025-3-27 14:23:30
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字形刻痕
发表于 2025-3-27 19:47:32
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stress-test
发表于 2025-3-28 01:36:41
Results from Algebraic Number Theory,In this chapter we formulate the theorems from class field theory for finite extensions that we shall need in the following, and we will transfer them to infinite extension as far as is necessary.
dowagers-hump
发表于 2025-3-28 05:57:34
The Maximal ,-Extension,The maximal .-extension . of a field . is the compositum (inside a fixed algebraic closure of .) of all finite .-extensions of ., i.e., of all normal (separable) extensions of . with .-power degree.
压碎
发表于 2025-3-28 07:51:43
Local Fields of Finite Type,In this chapter we study the maximal .-extension more closely in the case where . is a local field of finite type. Let Þ denote the prime ideal of . and χ(Þ) the characteristic of the residue class field of ..
火花
发表于 2025-3-28 11:58:39
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