On the embedding of left-symmetric algebras into differential perm-algebras

半素环嵌入半单阿廷环

Embeddings of semiprime rings into semisimple Artinian rings

本文给出半素环嵌入半单阿廷环的判据，引入并研究三类嵌入，证明最小嵌入为初等嵌入，并给出基于中心的新判据及最小嵌入的显式描述。

Superstability, noetherian rings and pure-semisimple rings

We uncover a connection between the model-theoretic notion of superstability and that of noetherian rings and pure-semisimple rings. We characterize noetherian rings via superstability of the class of left modules with embeddings. $\mathbf{Theorem.}$ For a ring $R$ the following are equivalent. - $R$ is left noetherian. - The class of left $R$-modules with embeddings is superstable. - For every $λ\geq |R| + \aleph_0$, there is $χ\geq λ$ such that the class of left $R$-modules with embeddings has uniqueness of limit models of cardinality $χ$. - Every limit model in the class of left $R$-modules…

不变嵌入与加权置换

Invariant embeddings and weighted permutations

该研究证明了酉矩阵共轭下不变的阿贝尔自伴矩阵代数可嵌入同不变性的极大阿贝尔自伴代数，并以此分析特定可交换矩阵的结构、刻画与加权置换酉等价的矩阵。

On superstability in the class of flat modules and perfect rings

We obtain a characterization of left perfect rings via superstability of the class of flat left modules with pure embeddings. $\mathbf{Theorem.}$ For a ring $R$ the following are equivalent. - $R$ is left perfect. - The class of flat left $R$-modules with pure embeddings is superstable. - There exists a $λ\geq (|R| + \aleph_0)^+$ such that the class of flat left $R$-modules with pure embeddings has uniqueness of limit models of cardinality $λ$. - Every limit model in the class of flat left $R$-modules with pure embeddings is $Σ$-cotorsion. A key step in our argument is the study of limit model…