论文标题
内态环通过最小的形态
Endomorphism rings via minimal morphisms
论文作者
论文摘要
我们证明，如果$ u：k \ rightarrow m $是左键的最小扩展，那么两个子环之间存在同构，$ \ textrm {end} _r^m（k）$和$ \ textrm {end} _r {end} _r _r^k（m） $ \ textrm {end} _r（m）$，他们的jacobson激进分子。这种同构用于在某些情况下从$ m $的内态循环中推断出$ k $的内态戒指的属性，例如$ k $在$ m，$ $ m，$ $ m，$ k $下不变时，$ k $在$ m $ m $ m $ $ m $的情况下是不变的。
We prove that if $u:K \rightarrow M$ is a left minimal extension, then there exists an isomorphism between two subrings, $\textrm{End}_R^M(K)$ and $\textrm{End}_R^K(M)$ of $\textrm{End}_R(K)$ and $\textrm{End}_R(M)$ respectively, modulo their Jacobson radicals. This isomorphism is used to deduce properties of the endomorphism ring of $K$ from those of the endomorphism ring of $M$ in certain situations such us when $K$ is invariant under endomorphisms of $M,$ or when $K$ is invariant under automorphisms of $M$.
