2022/04/07 by Nikken Prima Puspita, Indah Emilia Wijayanti, Puspita, Nikken Prima +2
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2204.03220
openalex publication_date 2022/04/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Let R be a commutative ring with unity and C be an R-coalgebra. The ring R is clean if every r∈ 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.