Hereditary and Formally Smooth Coalgebras |
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| Authors: | P. Jara L. Merino D. Llena D. Ştefan |
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| Affiliation: | (1) Department of Algebra, University of Granada, 18071 Granada, Spain;(2) Department of Geometry, University of Almería, 04120 Almeria, Spain;(3) Department of Mathematics, University of Bucharest, 14 Academiei Street, RO 010014 Bucharest, Romania |
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| Abstract: | We define formally smooth coalgebras and we study their relation with hereditary coalgebras. The main result of the paper establishes that a coalgebra with separable coradical is hereditary if and only if it is formally smooth if and only if it is the cotensor coalgebra  , where C0 is the coradical of C and N is a certain (C0,C0)–bicomodule. Presented by A. Verschoren Mathematics Subject Classifications (2000) primary: 16W30; secondary: 18G20. D. Ştefan: This author thanks the members of the Algebra Department of the University of Granada for their warm hospitality. He is especially grateful to Pascual Jara for the kind invitation to visit University of Granada. This research was partially supported by CERES, Contract 4-147. |
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| Keywords: | Hochschild dimension of coalgebras hereditary coalgebras formally smooth coalgebras |
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