Continuous semigroup structures on R, cancellative semigroups and bands

Up to isomorphism there is only one continuous group operation on R , as Aczél (Bull Soc Math Fr 76: 59–64, 1949 ) showed in 1949. In this paper we show that there are exactly three distinct continuous (weakly) cancellative semigroup structures on R modulo isomorphism. On the other hand, there are m...

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Bibliographic Details
Published in:Semigroup forum 2015-04, Vol.90 (2), p.518-531
Main Authors: Kobayashi, Yuji, Nakasuji, Yasuo, Takahasi, Sin-Ei, Tsukada, Makoto
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Research Article
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Summary:Up to isomorphism there is only one continuous group operation on R , as Aczél (Bull Soc Math Fr 76: 59–64, 1949 ) showed in 1949. In this paper we show that there are exactly three distinct continuous (weakly) cancellative semigroup structures on R modulo isomorphism. On the other hand, there are many continuous non-cancellative semigroup structures on R . We classify all ordered continuous bands (idempotent semigroups) on R . There are exactly eight (five) distinct ordered continuous band structures on R modulo isomorphism (and anti-isomorphism).
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-014-9624-x