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Submitted
October 9, 2021
Accepted
June 7, 2022
Published
July 31, 2022
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Abstract

Let R be a commutative ring with multiplicative identity and C be a coassociative and counital R-coalgebra with the α-condition. A clean comodules defined based on the cleanness on rings and modules. A C-comodule M is a clean comodule if the endomorphism ring of C-comodule M is clean. A clean R-coalgebra C is a clean comodule over itself i.e., if the endomorphism ring of C as a C-comodule is clean. For an idempotent e ∈ R, there are relations between the cleanness of eRe and R. It’s motivated us to investigate this condition for coalgebra. For any C, we can construct the R-coalgebra e ⇀C↼e where e is an idempotent element of dual algebra of C. Here, we show that the clean conditions of C implies the clean property of e ⇀C↼ e and vice versa.

Keywords

coalgebra clean coalgebra clean comodule corner ring

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How to Cite
Puspita, N. P., Wijayanti, I. E., & Surodjo, B. (2022). The Necessary and Sufficient Condition of Clean R-Coalgebra e⇀C↼e. Journal of the Indonesian Mathematical Society, 28(2), 215–220. https://doi.org/10.22342/jims.28.2.1066.215-220
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