Abstract
The fundamental theorem on coalgebras asserts that coalgebras are locally finite in the case where the ground ring is a field. We prove the local finiteness theorem of corings under the semihereditarity condition on the base algebra and the projectivity condition on a coring. This result generalizes not only the fundamental theorem on coalgebras but also Hazewinkel’s result on the local finiteness of coalgebras over a principal ideal domain and Bergman’s unpublished result on the local finiteness of corings over a semisimple Artinian ring.
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Kihara, H. A local finiteness theorem for corings over semihereditary rings. Arch. Math. 106, 507–513 (2016). https://doi.org/10.1007/s00013-016-0902-6
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DOI: https://doi.org/10.1007/s00013-016-0902-6