Open AccessThe Sufficient Conditions of The C*-Module C*m to become a C-Subcomodule
Author(s) -
N P Puspita,
I E Wijayanti,
B Surodjo
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1751/1/012001
Subject(s) - subcategory , coalgebra , commutative ring , mathematics , homomorphism , pure mathematics , ring (chemistry) , zero (linguistics) , functor , set (abstract data type) , free module , direct limit , algebra over a field , commutative property , discrete mathematics , computer science , chemistry , linguistics , programming language , philosophy , organic chemistry
Let R be a commutative ring with identity and M be a comodule over R -coalgebra C . It was already well-known that any C -comodule M is a module over dual algebra C* where C* is the set of all R -module homomorphisms from C to R . Furthermore, the category of comodule is a subcategory of the category of C* -module. Hence, any C -subcomodule of M is a C* -submodule of M , and the conversely is not true. For any non zero element m in M, C*m is a C* -submodule of M . In general, C*m is not to become a C -subcomodule of M . By using the theory of exact sequences in modules and the theory of categories, we give a condition such that C*m to be a C -subcomodule of M .