Noble inverse semigroups with bisimple core
type: Item
instance of: scholarly article
title: Noble inverse semigroups with bisimple core
zbMATH Open document ID: 0625.20053
DOI: 10.1007/BF02575014
author: Boris M. Schein
published in: Semigroup Forum
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134894
review text: An inverse semigroup is said to be noble if and only if it possesses a faithful transitive representation by one-to-one partial transformations on a set. An old problem - how to characterize noble inverse semigroups - is solved in the present paper for inverse semigroups with a bisimple (0- bisimple) ideal. A subset B of an inverse semigroup S is called a basis if each element of S is the least upper bound (with respect to the natural order on S) of a subset of B. The main result: an inverse semigroup S with a nonzero bisimple (0-bisimple) ideal B is noble if and only if B is a basis of S. The author also writes that a description of noble inverse semigroups in the general case will be considered in a separate publication.
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M30
zbMATH DE Number: 4015018
zbMATH Keywords: faithful transitive representation
zbMATH Keywords: one-to-one partial transformations
zbMATH Keywords: noble inverse semigroups
zbMATH Keywords: basis
MaRDI profile type: Publication
cites work: Q5564342
cites work: Q4126563
cites work: Q5635621
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description: scientific article; zbMATH DE number 4015018