步履蹒跚
发表于 2025-3-25 03:51:20
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连累
发表于 2025-3-25 07:55:34
Prime Ideals and Maximal IdealsAn ideal . in a ring . is called . if . ≠ . and . ∈ . implies . ∈ . or . ∈
Flat-Feet
发表于 2025-3-25 11:39:29
Finite FieldsThe . of a field . is the intersection of all the subfields of
剧毒
发表于 2025-3-25 17:04:02
Irreducible PolynomialsOur next project is to find some criteria that a polynomial be irreducible; this is usually difficult, and it is unsolved in general.
Minatory
发表于 2025-3-25 20:21:08
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保守
发表于 2025-3-26 01:05:39
Splitting FieldsWe have already observed that if F is a subfield of ., then . may be viewed as a vector space over
Ledger
发表于 2025-3-26 07:55:46
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议程
发表于 2025-3-26 09:28:38
The Galois GroupThe next lemma, though very easy to prove, is fundamental.
MODE
发表于 2025-3-26 16:40:48
Primitive Roots of UnityThe hypothesis in Theorem 40 that . contain certain roots of unity can be dropped, but we give a preliminary discussion from group theory before proving this.
赞成你
发表于 2025-3-26 18:29:45
Insolvability of the QuinticRecall Theorem A21: If . is a group having a solvable normal subgroup . such that . is solvable, then . is solvable. Here is the improved version of Theorem 40 which needs no assumption about roots of unity.