| 张玉林,姚海楼.森田六元组的几乎分裂序列[J].数学年刊A辑,2014,35(3):373~384 |
| 森田六元组的几乎分裂序列 |
| The Almost Split Sequences for the Morita Context |
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| DOI： |
| 中文关键词: 环,森田六元组,几乎分裂序列,既约同态 |
| 英文关键词:Rings, Morita context, Almost split sequence, Irreducible morphism |
| 基金项目:国家自然科学基金 (No.10971172, No.11271119)和北京市自然科学基金(No.1122002) |
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| 中文摘要: |
| 令$\Lambda_{1}$, $\Lambda_{2}$为两个环,$M$是$(\Lambda_{2}-\Lambda_{1})$-双模,且$N$是$(\Lambda_{1}-\Lambda_{2})$-双模.
六元组$\Gamma=(\Lambda_{1}$, $\Lambda_{2},N,M,\psi,\varphi)$是一个森田六元组.对于$\Gamma$的表示,确定其几乎分裂序列(也称AR-序列)
是非常重要的.
通过$\rmod \Lambda_{1}$和$\rmod \Lambda_{2}$的右(左)几乎分裂同态、既约同态构造$\Gamma$上的相应同态,
并进一步确定它的几乎分裂序列. |
| 英文摘要: |
| Let $\Lambda_{1}$, $\Lambda_{2}$ be rings, $M$ be a $(\Lambda_{2}-\Lambda_{1})$-bimodule and $N$ be a $(\Lambda_{1}-\Lambda_{2})$-bimodule. The six-tuple $\Gamma=(\Lambda_{1},\Lambda_{2},N,M,\psi,\varphi)$ is
a Morita context. In order to study the representation of $\Gamma$, it is important to determine its almost split sequences (i.e., AR-sequences). The authors construct
the corresponding morphisms in $\Gamma$ through the right (left) almost split morphisms and the irreducible morphisms in $\rmod \Lambda_1$ and $\rmod \Lambda_2$. Furthermore, its almost split sequences are determined. |
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