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- Title
THE NECESSARY AND SUFFICIENT CONDITION OF e ⇀ C ↼ e AS A CLEAN R-COALGEBRA.
- Authors
PUSPITA, NIKKEN P.; WIJAYANTI, INDAH EMILIA; SURODJO, BUDI
- 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.
- Subjects
IDEMPOTENTS; ASSOCIATIVE rings; ENDOMORPHISM rings; COMMUTATIVE rings
- Publication
Journal of the Indonesian Mathematical Society, 2022, Vol 28, Issue 2, p215
- ISSN
2086-8952
- Publication type
Article