当一个$\mathscr{S}$ -闭子模是一个直被加数时
When an $\mathscr{S}$-closed submodule is a direct summand
摘要：
众所周知，CLS-模的直和一般不是CLS-模。证明了如果$M=M_1\oplus M_2$，其中$M_1$和$M_2$是CLS-模，使得$M_1$和$M_2$是相对对象的（或$M_1$是$M_2$ -射的），则$M$是CLS-模，推广了一些已知的结果. Tercan [8]证明了如果一个模$M=M_{1}\oplus M_{2}$其中$M_{1}$和$M_{2}$是CS-模使得$M_{1}$是$M_{2}$ -内射的，则$M$是CS-模当且仅当$Z_{2}(M)$是CS-模.在这里，我们将表明，Tercan的说法是不正确的。
英文摘要：
It is well known that a direct sum of CLS-modules is not, in general, a CLS-module. It is proved that if $M=M_1\oplus M_2$, where $M_1$ and $M_2$ are CLS-modules such that $M_1$ and $M_2$ are relatively ojective (or $M_1$ is $M_2$-ejective), then $M$ is a CLS-module and some known results are generalized. Tercan [8] proved that if a module $M=M_{1}\oplus M_{2}$ where $M_{1}$ and $M_{2}$ are CS-modules such that $M_{1}$ is $M_{2}$-injective, then $M$ is a CS-module if and only if $Z_{2}(M)$ is a CS-module. Here we will show that Tercan's claim is not true.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
