[過去ﾛｸﾞ] 純粋・応用数学（含むガロア理論）3 (1002ﾚｽ)
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892(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/08/29(土)13:27 ID:T0GrcKp2(3/15) AAS
>>891
つづき

P210
7. FREE R-MODULES
Undoubtedly, the modules that are most familiar to the reader are vector spaces
over a field. Probably the most distinctive feature of the theory of vector spaces is
that every vector space has a basis. After generalizing the notion of a basis from
省23

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893(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/08/29(土)13:28 ID:T0GrcKp2(4/15) AAS
>>892
つづき

(iii) If {rs}s∈S is an almost zero family of elements of R such that Σs∈S rss =0,
then rs =0 for each s in S.
(iv) If {rs}s∈S and {r's}s∈S are two almost zero families of elements of R such
that Σs∈S rss = Σs∈S r'ss, then rs=r's for all s in S.

We now give some examples to illustrate various types of linearly indepen
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