论文标题
均匀的$ s $ - 非核心戒指
Uniformly $S$-Noetherian rings
论文作者
论文摘要
让$ r $为戒指，$ s $乘以$ r $的乘法子集。然后，$ r $被称为均匀的$ s $ -noetherian（$ u $ - $ s $ -s -noetherian用于缩写）戒指，只要存在一个元素$ s \ in s $中，以至于对于任何理想的$ i $ i $ i $ i $ i $ i $ r $，$ si \ subseteq k $，用于某些有限生成的$ k $ k $ $ i $ i $ $ $ $ $ $。我们为$ U $ - $ s $ -noetherian戒指提供Eakin-Nagata-formanek定理。此外，给出了$ U $ - $ S $ -Noetherian物业在几个戒指构造中。还介绍和研究了$ u $ - $ s $ imentive模块的概念。最后，我们获得了Cartan-Eilenberg-bass定理的均匀$ s $ -noetherian戒指。
Let $R$ be a ring and $S$ a multiplicative subset of $R$. Then $R$ is called a uniformly $S$-Noetherian ($u$-$S$-Noetherian for abbreviation) ring provided there exists an element $s\in S$ such that for any ideal $I$ of $R$, $sI \subseteq K$ for some finitely generated sub-ideal $K$ of $I$. We give the Eakin-Nagata-Formanek Theorem for $u$-$S$-Noetherian rings. Besides, the $u$-$S$-Noetherian properties on several ring constructions are given. The notion of $u$-$S$-injective modules is also introduced and studied. Finally, we obtain the Cartan-Eilenberg-Bass Theorem for uniformly $S$-Noetherian rings.
