On subamalgams of partially ordered monoids

Al Subaiei, Bana and Renshaw, James (2022) On subamalgams of partially ordered monoids. Semigroup Forum, 105 (3), 619-645. (doi:10.1007/s00233-022-10321-2).

Record type: Article

Abstract

The study of pomonoid amalgams was initiated by Fakhuruddin in the 1980s and subsequently extended by Bulman-Fleming, Sohail and the authors in the 2000s. We further investigate pomonoids amalgams and in particular we consider the concept of subpomonoid amalgams possessing a suitable ordered version of the unitary property. If [U; T ₁, T ₂] is an amalgam of subpomonoids of the amalgam [U; S ₁, S ₂] we consider the question of whether the free product of the pomonoid amalgam [U; T ₁, T ₂] is poembeddable in the free product of the pomonoid amalgam [U; S ₁, S ₂] , giving a sufficient condition in terms of strongly pounitary subpomonoids.

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Accepted/In Press date: 7 October 2022

e-pub ahead of print date: 25 October 2022

Published date: December 2022

Additional Information: Funding Information: This work formed part of the PhD thesis of the first named author submitted to the University of Southampton and written under the supervision of Dr. James Renshaw. The authors would like to thank the anonymous referee for their useful comments. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: Amalgam, Pomonoid, Pounitary, Pullback

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