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2. Strong separativity over exchange rings
- Creator:
- Chen, Huanyin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- strong separativity, exchange ring, and regular ring
- Language:
- English
- Description:
- An exchange ring $R$ is strongly separative provided that for all finitely generated projective right $R$-modules $A$ and $B$, $A\oplus A\cong A \oplus B\Rightarrow A\cong B$. We prove that an exchange ring $R$ is strongly separative if and only if for any corner $S$ of $R$, $aS+bS=S$ implies that there exist $u,v\in S$ such that $au=bv$ and $Su+Sv=S$ if and only if for any corner $S$ of $R$, $aS+bS=S$ implies that there exists a right invertible matrix $\begin{pmatrix} a&b\\ *&* \end{pmatrix} \in M_2(S)$. The dual assertions are also proved.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public