[過去ﾛｸﾞ] 純粋・応用数学（含むガロア理論）3 (1002ﾚｽ)
上下前次1-新
抽出解除 ﾚｽ栞

---

このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索 歴削→次ｽﾚ 栞削→次ｽﾚ 過去ﾛｸﾞﾒﾆｭｰ

---

897(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/08/29(土)13:37 ID:T0GrcKp2(8/15) AAS
>>896
つづき

Basic Properties 8.4
Let R be an arbitrary ring and M a nonzero R-module. The following conditions
are equivalent:
(a) M is generated by each nonzero element in M.
(b) For every R-module X, every morphism f:X→M is either zero or an
省23

---

898(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/08/29(土)13:37 ID:T0GrcKp2(9/15) AAS
>>897
つづき

Hence, R is a division ring because we have already seen that a ring R is a division
ring if and only if the R-module R is a simple R-module. Thus, our problem of
showing that a nonzero ring R is a division ring if every R-module is free is solved
once we establish that every nonzero ring has a simple module. To this end it is
convenient to have the following.
省22

---

上下前次1-新書関写板覧索設栞歴

---

ｽﾚ情報 赤ﾚｽ抽出 画像ﾚｽ抽出 歴の未読ｽﾚ AAｻﾑﾈｲﾙ

---

ぬこの手 ぬこTOP 2.374s*