论文标题
连续的综合
Continuous Comodules
论文作者
论文摘要
让$ r $成为具有团结的换向戒指，$ c $是$ r $ -Coalgebra。如果每个$ r \ in r $中的每个$ r \ r \是一个单位的总和，则是$ r $ $ r $的总和。如果$ m $ $ $ r $ $ $ $ $ $ $ $ $ $ M $ m $ $ m $ m $是干净的。此外，每个连续模块都很干净。我们将这个想法修改为综合和煤堡案例。如果$ c $ m $ $ c $ co $ - 编码的内态为$ m $干净，则称为干净的comodule。我们引入了连续的综合，并证明了每个连续的综合物都是一个干净的综合。
Let $R$ be a commutative ring with unity and $C$ be an $R$-coalgebra. The ring $R$ is clean if every $ r\in R $ is the sum of a unit and an idempotent element of $R$. An $R$-module $M$ is clean if the endomorphism ring of $M$ over $R$ is clean. Moreover, every continuous module is clean. We modify this idea to the comodule and coalgebra cases. A $C$-comodule $M$ is called a clean comodule if the $C$-comodule endomorphisms of $M$ are clean. We introduced continuous comodules and proved that every continuous comodules is a clean comodule.
