Clean coalgebras and clean comodules of finitely generated projective modules
Let \(R\) be a commutative ring with multiplicative identity and \(P\) is a finitely generated projective \(R\)-module. If \(P^{\ast}\) is the set of \(R\)-module homomorphism from \(P\) to \(R\), then the tensor product \(P^{\ast}\otimes_{R}P\) can be considered as an \(R\)-coalgebra. Furthermore,...
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| Date: | 2021 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2021
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1415 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | Let \(R\) be a commutative ring with multiplicative identity and \(P\) is a finitely generated projective \(R\)-module. If \(P^{\ast}\) is the set of \(R\)-module homomorphism from \(P\) to \(R\), then the tensor product \(P^{\ast}\otimes_{R}P\) can be considered as an \(R\)-coalgebra. Furthermore, \(P\) and \(P^{\ast}\) is a comodule over coalgebra \(P^{\ast}\otimes_{R}P\). Using the Morita context, this paper give sufficient conditions of clean coalgebra \(P^{\ast}\otimes_{R}P\) and clean \(P^{\ast}\otimes_{R}P\)-comodule \(P\) and \(P^{\ast}\). These sufficient conditions are determined by the conditions of module \(P\) and ring \(R\). |
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