Factorizable inverse monoids.
type: Item
instance of: scholarly article
title: Factorizable inverse monoids.
zbMATH Open document ID: 1202.20067
published in: Semigroup Forum
publication date: 2010-07-06T00:00:00Z
full work available at URL: Survey Revision 07.pdf
review text: An inverse monoid \(S\) is called `factorizable' provided that it decomposes into a product \(UE\) of its group \(U\) of units and its semi-lattice \(E\) of idempotents. The paper under review is a survey of the algebraic theory of factorizable inverse monoids. The paper starts with a short historical overview. This goes over to the structure theory of factorizable inverse monoids, where the author describes properties of Green's relations, subgroups and idempotents. The next part contains a discussion on submonoids, congruences and presentations. In the last part of the paper the author presents many examples, including (the factorizable part of) the symmetric inverse monoid, the dual symmetric inverse monoid, the coset monoid, the Galois inverse monoid, reflection monoids and Renner monoids.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 5730949
zbMATH Keywords: factorizable inverse monoids
zbMATH Keywords: factorizable monoids
zbMATH Keywords: symmetric monoids
zbMATH Keywords: restrictions
zbMATH Keywords: coset monoids
zbMATH Keywords: presentations
author: D. G. Fitz-Gerald
MaRDI profile type: Publication
OpenAlex ID: W2028587534
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DOI: 10.1007/S00233-009-9177-6
description: scientific article; zbMATH DE number 5730949