Abstract—The purpose of this paper is to investigate FC-projective comodules and FC-projective dimensions. We introduce the concepts of copure exact sequences and FC-projective comodules, and give some equivalent characterizations of FC-projective modules. We also define FC-projective dimensions, which is similar to projective dimensions. We characterize semihereditary and coregular coalgebras related to FC-projective comodules.

Keywords—Coalgebra, comodule, FC-projective comodule, FC-projective dimension, semihereditary coalgebra, coregular coalgebra

Cite:Qianqian Yuan, Hailou Yao, "FC-Projective Comodules and FC-Projective Dimensions," International Journal of Applied Physics and Mathematics, vol. 14, no. 1, pp. 12-19, 2024.

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