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The lattice of positive quasi-orders on a semigroup

✍ Scribed by Miroslav Ćirić; Stojan Bogdanović

Publisher
The Hebrew University Magnes Press
Year
1997
Tongue
English
Weight
427 KB
Volume
98
Category
Article
ISSN
0021-2172

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Construction of lattice orders on the semigroup ring of a positive rooted monoid
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Lattice orders on the semigroup ring of a positive rooted monoid are constructed, and it is shown how to make the monoid ring into a lattice-ordered ring with squares positive in various ways. It is proved that under certain conditions these are all of the lattice orders that make the monoid ring in

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It is well known that the free group on a non-empty set can be totally ordered and, further, that each compatible latttice ordering on a free group is a total ordering. On the other hand, Saitô has shown that no non-trivial free inverse semigroup can be totally ordered. In this note we show, however