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Title
On positive commutative tomonoids
AuthorVetterlein, Thomas
Published in
Algebra universalis, 2016, Vol. 75, Issue 4, page 381-404
PublishedSpringer, 2016
LanguageEnglish
Document typeJournal Article
Keywords (EN)totally ordered monoid / direction cone
Project-/ReportnumberI 1923-N25
ISSN1420-8911
URNurn:nbn:at:at-ubl:3-1433 Persistent Identifier (URN)
DOI10.1007/s00012-016-0377-0 
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 The work is publicly available
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On positive commutative tomonoids [0.88 mb]
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Abstract (English)

We discuss totally ordered monoids (or tomonoids, for short) that are commutative, positive, and finitely generated. Tomonoids of this kind correspond to certain preorders on free commutative monoids. In analogy to positive cones of totally ordered groups, we introduce direction cones to describe the preorders in question and we establish between both notions a Galois connection. In particular, we show that any finitely generated positive commutative tomonoid is the quotient of a tomonoid arising from a direction cone. We furthermore have a closer look at formally integral tomonoids and at nilpotent tomonoids. In the latter case, we modify our approach in order to obtain a description that is based on purely finitary means.

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CC-BY-License (4.0)Creative Commons Attribution 4.0 International License