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The Archimedean property in an ordered semigroup

Published online by Cambridge University Press:  09 April 2009

Tôru Saitô
Tôru Saitô
Affiliation:
Tokyo Gakugei University
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By an ordered semigroup we mean a semigroup with a simple order which is compatible with the semigroup operation. Several authors, for example Alimov [1], Clifford [2], Conrad [4] and Hion [7], studied the archimedean property in some special kinds of ordered semigroups. For a general ordered semigroup, Fuchs [6] defined the archimedean equivalence as follows: a ~ b if and only if one of the four conditionsholds for some positive integer n.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 3 , August 1968 , pp. 547 - 556
Copyright
Copyright © Australian Mathematical Society 1968

References

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