森田六元组的几乎分裂序列

令ΛA_1,Λ_2为两个环,M是(A_2-Λ_1)-双模,且N是(Λ_1-Λ_2)-双模.六元组Γ=(Λ_1,Λ_2,N,M,ψ,φ)是一个森田六元组.对于Γ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modΛ_1和modΛ_2的右(左)几乎分裂同态、既约同态构造Γ上的相应同态,并进一步确定它的几乎分裂序列.

The Almost Split Sequences for the Morita Context

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.