| 廖军,杨艳,刘合国.带有限性条件Abel群的自同态环和自同构群[J].数学年刊A辑,2011,32(6):665~678 |
| 带有限性条件Abel群的自同态环和自同构群 |
| Endomorphism Rings and Automorphism Groups of Abelian Groups with Finiteness Conditions |
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| DOI： |
| 中文关键词: 自同构群 自同态环 可解 幂零 |
| 英文关键词:Automorphism group Endomorphism ring Solvable Nilpotent |
| 基金项目:国家自然科学基金(No10971054)资助的项目 |
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| 中文摘要: |
| 给出了带极大或极小条件的
Abel群$A$的自同构群以及自同态环的相伴Lie环是可解或幂零的充要条件.
同时也给出了群$A=Q_{\pi_1}\oplus {Q}_{\pi_2}\oplus \cdots \oplus
Q_{\pi_r}$的自同构群是可解或幂零的充要条件,
以及群$A$的自同态环的相伴Lie环是可解或幂零的充要条件. |
| 英文摘要: |
| Let $A$ be an Abelian group with maximum or minimum condition. The authors
give necessary and sufficient conditions
for the automorphism group (resp. Lie ring associated with the endomorphism ring)
being solvable (resp. nilpotent).
Moreover, necessary and sufficient conditions
for the automorphism group (resp. Lie ring associated with the endomorphism ring)
being solvable (resp. nilpotent)
for $A=Q_{\pi_1}\oplus {Q}_{\pi_2}\oplus \cdots \oplus
Q_{\pi_r}$ are also given. |
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