论文标题
部分可观测时空混沌系统的无模型预测
Distributive Invariant Centrally Essential Rings
论文作者
论文摘要
近年来，在环理论中对中央必不可少的环进行了深入研究。特别是，他们发现在同源代数，群环和环的结构理论中的应用。本质上的中心环强烈扩展了通勤戒指的类别。对于此类环，许多最近的论文包含了RING理论中一些重要问题的积极答案，这些问题以前对通勤环和一般情况下的负面答案有积极的答案。这项工作专门用于类似的主题。对右noetherian的熟悉描述，正确的分配中心基本环在更大的戒指上概括了。让$ a $是Prime Radical $ P（a）$的戒指。 It is proved that $A$ is a right distributive, right invariant centrally essential ring and $P(A)$ is a finitely generated right ideal such that the factor-ring $A/P(A)$ does non contain an infinite direct sum of non-zero ideals if and only if $A=A_1\times\cdots\times A_n$, where every ring $A_k$ is either a commutative Prüfer domain or an Artinian单个环。
In recent years, centrally essential rings have been intensively studied in ring theory. In particular, they find applications in homological algebra, group rings, and the structural theory of rings. The class of essentially central rings strongly extends the class of commutative rings. For such rings, a number of recent papers contain positive answers to some important questions from ring theory that previously had positive answers for commutative rings and negative answers in the general case. This work is devoted to a similar topic. A familiar description of right Noetherian, right distributive centrally essential rings is generalized on a larger class of rings. Let $A$ be a ring with prime radical $P(A)$. It is proved that $A$ is a right distributive, right invariant centrally essential ring and $P(A)$ is a finitely generated right ideal such that the factor-ring $A/P(A)$ does non contain an infinite direct sum of non-zero ideals if and only if $A=A_1\times\cdots\times A_n$, where every ring $A_k$ is either a commutative Prüfer domain or an Artinian uniserial ring.
