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Forum Mathematicum

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Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Volume 30, Issue 6

Issues

Idempotence of finitely generated commutative semifields

Vítězslav KalaORCID iD: http://orcid.org/0000-0001-5515-6801 / Miroslav KorbelářORCID iD: http://orcid.org/0000-0002-9751-3261
Published Online: 2018-07-12 | DOI: https://doi.org/10.1515/forum-2017-0098

Abstract

We prove that a commutative parasemifield S is additively idempotent, provided that it is finitely generated as a semiring. Consequently, every proper commutative semifield T that is finitely generated as a semiring is either additively constant or additively idempotent. As part of the proof, we use the classification of finitely generated lattice-ordered groups to prove that a certain monoid associated to the parasemifield S has a distinguished geometrical property called prismality.

Keywords: Commutative semiring; parasemifield; idempotent; convex; affine monoid

MSC 2010: 12K10; 16Y60; 20M14; 11H06; 52A20

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About the article


Received: 2017-05-03

Revised: 2018-01-30

Published Online: 2018-07-12

Published in Print: 2018-11-01


The first author was supported by Neuron Impulse award and by Charles University Research Centre program UNCE/SCI/022.


Citation Information: Forum Mathematicum, Volume 30, Issue 6, Pages 1461–1474, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0098.

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