On free products and amalgams of pomonoids
On free products and amalgams of pomonoids
The study of amalgamation in the category of partially ordered monoids was initiated by Fakhuruddin in the 1980s. In 1986 he proved that, in the category of commutative pomonoids, every absolutely flat commutative pomonoid is a weak amalgmation base and every commutative pogroup is a strong amalgamation base. Some twenty years later, Bulman-Fleming and Sohail in 2011 extended this work to what they referred to as pomonoid amalgams. In particular, they proved that pogroups are poamalgmation bases in the category of pomonoids. Sohail, also in 2011, proved that absolutely poflat commutative pomonoids are poamalgmation bases in the category of commutative pomonoids. In the present article, we extend the work on pomonoid amalgams by generalizing the work of Renshaw on amalgams of monoids and extension properties of acts over monoids.
2455-2474
Al Subaiei, Bana
b7621a63-1d65-4780-9a97-ae2c68c6be43
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
Al Subaiei, Bana
b7621a63-1d65-4780-9a97-ae2c68c6be43
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
Abstract
The study of amalgamation in the category of partially ordered monoids was initiated by Fakhuruddin in the 1980s. In 1986 he proved that, in the category of commutative pomonoids, every absolutely flat commutative pomonoid is a weak amalgmation base and every commutative pogroup is a strong amalgamation base. Some twenty years later, Bulman-Fleming and Sohail in 2011 extended this work to what they referred to as pomonoid amalgams. In particular, they proved that pogroups are poamalgmation bases in the category of pomonoids. Sohail, also in 2011, proved that absolutely poflat commutative pomonoids are poamalgmation bases in the category of commutative pomonoids. In the present article, we extend the work on pomonoid amalgams by generalizing the work of Renshaw on amalgams of monoids and extension properties of acts over monoids.
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pomonoid_free_products_revision_2.pdf
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Submitted date: 20 December 2013
Accepted/In Press date: 29 April 2016
e-pub ahead of print date: 29 April 2016
Organisations:
Pure Mathematics
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Local EPrints ID: 360761
URI: http://eprints.soton.ac.uk/id/eprint/360761
ISSN: 0092-7872
PURE UUID: 6ff81041-cf04-4693-b6b9-620047504731
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Date deposited: 03 Jan 2014 16:41
Last modified: 15 Mar 2024 02:40
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Author:
Bana Al Subaiei
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