Continuous Comodules
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Abstract
Let $R$ be a commutative ring with unity and $C$ an $R$-coalgebra. The ring $R$ is clean if every elements $r$ 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 adapt this idea to comodules and coalgebras. A $C$-comodule $M$ is called a clean comodule if the $C$-comodule endomorphisms of $M$ are clean. We introduce continuous comodules and proved that every continuous comodules is a clean comodules.
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