Abstract.
In this note, the new concepts of C-bases (resp., BC-bases, L-bases) which are special kinds of abstract bases are introduced. It is proved that the round ideal completion of a C-basis (resp., BC-basis, L-basis) is a continuous lattice (resp., bc-domain, L-domain). Furthermore, representation theorems of continuous lattices (resp., bc-domains, L-domains) by means of the round ideal completions of C-bases (resp., BC-bases, L-bases) are obtained.
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Received August 29, 2006; accepted in final form December 28, 2006.
Supported by the NSF of China (10371106, 60774073) and by the Fund (S0667-082) from Nanjing University of Aeronautics and Astronautics.
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Xu, L., Mao, X. When do abstract bases generate continuous lattices and L-domains. Algebra univers. 58, 95–104 (2008). https://doi.org/10.1007/s00012-008-2042-8
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DOI: https://doi.org/10.1007/s00012-008-2042-8