论文标题
Baer和Dual Baer模块的新方法
A new approach to Baer and dual Baer modules
论文作者
论文摘要
令$ r $为戒指。事实证明，当且仅当每个确切的序列$ 0 \ rightarrow x \ rightarrow m \ rightarrow y \ rightarrow y \ rightarrow 0 $ with $ y \ in $ cog $（m_r）$（m_r）$（resp。这表明（双重）Baer是莫里塔不变的财产。随着越来越多的应用程序，研究了$ r $ -module $ m^+ $ = hom $ _ {\ bbb z}}（m，{\ bbb q}/{\ bbb z}）$的$ r $是von noumann常规环，如果$ r^+ $是baer $ r-r-r-r r r r $ mmod。研究并确定BAER（分别为双BAER）模块时，研究并确定了（弱）链条条件的BAER模块 是相互正交质数（分别联合总理）模块的直接总和。有限生成的双BAER模块在交换环上是研究
Let $R$ be a ring. It is proved that an $R$-module $M$ is Baer (resp. dual Baer) if and only if every exact sequence $0\rightarrow X\rightarrow M\rightarrow Y\rightarrow 0$ with $Y\in$ Cog$(M_R)$ (resp. $X\in$ Gen$(M_R)$) splits. This shows that being (dual) Baer is a Morita invariant property. As more applications, the Baer condition for the $R$-module $M^+ $ = Hom$_{\Bbb Z}(M,{\Bbb Q}/{\Bbb Z})$ is investigated and shown that $R$ is a von Neumann regular ring, if $R^+$ is a Baer $R$-module. Baer modules with (weak) chain conditions are studied and determined when a Baer (resp. dual baer) module is a direct sum of mutually orthogonal prime (resp. co-prime) modules. Finitely generated dual Baer modules over commutative rings are studeid
