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arXiv · 2204.03220

Continuous Comodules

Nikken Prima Puspita·Indah Emilia Wijayanti·Budi Surodjo
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Abstract

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.

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Nikken Prima Puspita, Indah Emilia Wijayanti, Budi Surodjo. 2022-04-07. Continuous Comodules. https://arxiv.org/abs/2204.03220

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