论文标题
涵盖课程和单性模块
Covering classes and uniserial modules
论文作者
论文摘要
我们将最小生成集的最小生成集应用于研究添加$（u_r）$的存在 - 单次模块$ u_r $的封面。如果$ u_r $是环$ r $上的一个单个单右模块，则$ s：= $ end $（u_r）$最多具有两个最大（右，左，双面）理想的最大值：一个是所有内态的集合$ i $，这些$ i $不是注射性的，而另一种是所有n nesomorphist $ u__ $ u__ $ u__ $ u__的$ k $ curmorphists的$ u__ $ u__ $ u__ $ u _ b的$ k $。我们证明，如果$ u_r $是有限生成的，或Artinian或$ i \ subset k $，则类别添加$（u_r）$在且仅当其在直接限制下关闭时才覆盖。此外，我们研究了Artinian Uniserial模块的内态环，给出了几个例子。
We apply minimal weakly generating sets to study the existence of Add$(U_R)$-covers for a uniserial module $U_R$. If $U_R$ is a uniserial right module over a ring $R$, then $S:=$End$ (U_R)$ has at most two maximal (right, left, two-sided) ideals: one is the set $I$ of all endomorphisms that are not injective, and the other is the set $K $ of all endomorphisms of $U_R$ that are not surjective. We prove that if $U_R$ is either finitely generated, or artinian, or $I \subset K$, then the class Add$(U_R)$ is covering if and only if it is closed under direct limit. Moreover, we study endomorphism rings of artinian uniserial modules giving several examples.
