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Localization in coalgebras. Applications to finiteness conditions

J. Gomez-Torrecillas·C. Nastasescu·B. Torrecillas
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Abstract

The injective right comodules appearing in the minimal injective resolution of a finite-dimensional comodule need not to be of finite dimension or even quasi-finite. The obstruction here is that factor comodules of quasi-finite comodules are not in general quasi-finite. This note is mainly devoted to the study of coalgebras for which the class of all quasi-finite right comodules is closed under factor comodules. A major tool here is the local study, in the sense of abstract localization, of the comodules which have all their factors quasi-finite.

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J. Gomez-Torrecillas, C. Nastasescu, B. Torrecillas. 2004-03-15. Localization in coalgebras. Applications to finiteness conditions. https://arxiv.org/abs/math/0403248

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