The right dual of left \(C\)-\(rpp\) semigroups
type: Item
instance of: scholarly article
title: The right dual of left \(C\)-\(rpp\) semigroups
zbMATH Open document ID: 0903.20035
DOI: 10.1007/BF02882566
published in: Chinese Science Bulletin
publication date: 1998-02-10T00:00:00Z
review text: A semigroup \(S\) is said to be \(rpp\) if every principal right ideal \(aS^1\), regarded as a right \(S\)-system, is projective. Call an \(rpp\) semigroup \(S\) a \(C\)-\(rpp\) semigroup if its idempotents lie in the centre of \(S\). In this paper, the author defines the right \(C\)-\(rpp\) semigroups by using \((\ell)\)-Green's relations and observes that the right \(C\)-\(rpp\) semigroups are the dual of the left \(C\)-\(rpp\) semigroups [see \textit{Y. Gou}, \textit{K.-P. Shum} and \textit{P. Zhu}, Semigroup Forum 50, No. 1, 9-23 (1995; Zbl 0821.20046)]. The crucial point is that the right \(C\)-\(rpp\) semigroups and left \(C\)-\(rpp\) semigroups are not symmetric, for instance, \({\mathcal L}^{(1)}={\mathcal J}^{(1)}\) on left \(C\)-\(rpp\) semigroups but \({\mathcal L}^{(1)},{\mathcal R}^{(1)}\nsubseteq{\mathcal D}^{(1)}={\mathcal J}^{(1)}\) on right \(C\)-\(rpp\) semigroups.
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M12
zbMATH DE Number: 1106392
zbMATH Keywords: right \(S\)-systems
zbMATH Keywords: right \(C\)-\(rpp\) semigroups
zbMATH Keywords: Green relations
zbMATH Keywords: principal right ideals
zbMATH Keywords: idempotents
author: Y. Q. Guo
reviewed by: K. P. Shum
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1106392