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Title
Rees coextensions of finite tomonoids and free pomonoids
AuthorVetterlein, Thomas
EditorPetrik, Milan
Published in
Semigroup Forum, 2018, Vol. 97, Issue 183, page 1-23
PublishedSpringer US, 2018
LanguageEnglish
Document typeJournal Article
Keywords (EN)Totally ordered monoid Tomonoid Rees congruence Rees coextension Free pomonoid Finite-valued logic
ISSN1432-2137
URNurn:nbn:at:at-ubl:3-412 Persistent Identifier (URN)
DOI10.1007/s00233-018-9972-z 
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 The work is publicly available
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Abstract (English)

A totally ordered monoid, or tomonoid for short, is a monoid endowed with a compatible total order. We reconsider in this paper the problem of describing the one-element Rees coextensions of a finite, negative tomonoid S, that is, those tomonoids that are by one element larger than S and whose Rees quotient by the poideal consisting of the two smallest elements is isomorphic to S. We show that any such coextension is a quotient of a pomonoid R(S) , called the free one-element Rees coextension of S. We investigate the structure of R(S) and describe the relevant congruences. We moreover introduce a finite family of finite quotients of R(S) from which the coextensions arise in a particularly simple way.

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