Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T00:03:34.403Z Has data issue: false hasContentIssue false

Ordered Semigroups

Published online by Cambridge University Press:  22 January 2016

Paul Conrad*
Affiliation:
Tulane University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

1. Introduction. In this paper order will always mean linear or total order, and, unless otherwise stated, the composition of any semigroup will be denoted by +. A semigroup S is an ordered semigroup (notation o.s.) if S is an ordered set and for all a, b, c in S

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

[1] Alimov, N. G., On ordered semigroups, Izv. Akad. Nauk SSSR Ser. Mat. 14 (1950), 569576.Google Scholar
[2] Chehata, C. G., On ordered semigroups, J. London Math. Soc. 28 (1953), 353356.Google Scholar
[3] Clifford, A. H., Bands of semigroups, Proc. Amer. Math. Soc. 5 (1954), 499504.Google Scholar
[4] Clifford, A. H., Totally ordered commutative semigroups, Bull. Amer. Math. Soc. 64 (1958), 305316.CrossRefGoogle Scholar
[5] Conrad, P., Extensions of ordered groups, Proc. Amer. Math. Soc. 6 (1955), 516528.Google Scholar
[6] Conrad, P., Semigroups of real numbers, (to appear).Google Scholar
[7] Everett, C. J., A note on a result of L. Fuchs on ordered groups, Amer. J. Math. 73 (1950), 216.CrossRefGoogle Scholar
[8] Ore, O., Linear equations in non-commutative fields, Annals Math. 32 (1931), 463477.Google Scholar
[9] Vinogradov, A. A., On the theory of ordered semigroups, Ivanov. Gos. Ped. Inst. Uc. Zap. Fiz. Mat. Nauki 4 (1953) 1921.Google Scholar