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Hereditary and Formally Smooth Coalgebras

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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 \(T_{C_{0}}(N)\) , where C0 is the coradical of C and N is a certain (C0,C0)–bicomodule.

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Authors and Affiliations

  1. Department of Algebra, University of Granada, 18071, Granada, Spain

    P. Jara & L. Merino

  2. Department of Geometry, University of Almería, 04120, Almeria, Spain

    D. Llena

  3. Department of Mathematics, University of Bucharest, 14 Academiei Street, RO 010014, Bucharest, Romania

    D. Ştefan

Authors
  1. P. Jara
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  2. L. Merino
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  3. D. Llena
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  4. D. Ştefan
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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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Jara, P., Merino, L., Llena, D. et al. Hereditary and Formally Smooth Coalgebras. Algebr Represent Theor 8, 363–374 (2005). https://doi.org/10.1007/s00000-005-8110-3

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  • DOI: https://doi.org/10.1007/s00000-005-8110-3

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