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Communications in Algebra Volume 29, 2001 - Issue 4
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Original Articles

DISCRETE ORDERINGS AND COMMUTATIVE MONOIDS

Athanassios Tzouvaras Dept. of Mathematics, Univ. of Thessaloniki, Thessaloniki, 540 06, Greece
Pages 1395-1407 | Received 01 Oct 1999, Published online: 16 Aug 2006
 
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Abstract

We show that a countable totally and discretely ordered set with first element inherently carries the structure of an ordered commutative euclidean monoid, provided its order type is of a certain kind. As an application we specify the order types of all discretely ordered sets which can be expanded to ordered commutative euclidean monoids.

Acknowledgments

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