A local finiteness theorem for corings over semihereditary rings

作者：Kihara Hiroshi^*

来源：ARCHIV DER MATHEMATIK, 2016, 106(6): 507-513.

DOI：10.1007/s00013-016-0902-6

• The fundamental theorem on coalgebras
• Coring
• Semihereditary ring

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but also Hazewinkel's result on the local finiteness of coalgebras over a principal ideal domain and Bergman's unpublished result on the local finiteness of corings over a semisimple Artinian ring.

• 出版日期2016-6