TY - JOUR AU - Puspita, Nikken Prima AU - Wijayanti, Indah E AU - Surodjo, Budi PY - 2022/07/31 Y2 - 2024/03/29 TI - The Necessary and Sufficient Condition of Clean R-Coalgebra e⇀C↼e JF - Journal of the Indonesian Mathematical Society JA - JIMS VL - 28 IS - 2 SE - Articles DO - 10.22342/jims.28.2.1066.215-220 UR - https://jims-a.org/index.php/jimsa/article/view/1066 SP - 215-220 AB - <p>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.</p> ER -