喷出
发表于 2025-3-23 11:52:33
,§ VIII,Theorem II.1 shows that every subgroup . of . is either 0 or generated by its smallest element .0. in the latter case it is generated by . or also by —., but by no other element of . For cyclic groups, we have:
falsehood
发表于 2025-3-23 16:22:00
,§ IX,In order to consider polynomials with coefficients in a field ., and equations over such fields, we begin by reviewing some elementary properties of polynomials over an arbitrary field .; these are independent of the nature of that field, and quite analogous to the properties of integers described above in §§ II, III, IV.
Annotate
发表于 2025-3-23 19:19:53
,§ X,Let G be a group of order m. If, for every divisor d of m, there are no more than d elements of G satisfying x.=1, G is cyclic.
欲望
发表于 2025-3-24 01:14:42
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follicular-unit
发表于 2025-3-24 05:31:51
Textbook 1979t the problem sessions so on became desultory. v vi Weekly notes were written up by Max Rosenlicht and issued week by week to the students. Rather than a literal reproduction of the course, they should be regarded as its skeleton; they were supplemented by references to stan dard text-books on alge
威胁你
发表于 2025-3-24 08:18:46
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欢笑
发表于 2025-3-24 12:34:50
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使激动
发表于 2025-3-24 17:47:55
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goodwill
发表于 2025-3-24 21:19:42
,§ XI,vial, we assume .≠0. If then, in the field ., . is a solution of x.=a, an element . of . is also a solution if and only if ...1. Therefore, if x.=a has a solution in ., it has as many solutions as . contains .. roots of unity, i.e. roots of ...1.
变异
发表于 2025-3-25 00:19:22
,§ XII,onsisting of the classes (±1 mod . we apply to . and . the definitions and lemma of § VIII. If . is an element of ., it belongs to one and only one coset . this consists of the two elements (±. mod . there are . such cosets, viz., the cosets (±1 mod .), (±2 mod .),...(±. mod .). If, in each coset, w