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IDEALS AND FINITENESS CONDITIONS FOR SUBSEMIGROUPS

Published online by Cambridge University Press:  13 August 2013

R. GRAY,
V. MALTCEV,
J. D. MITCHELL and
N. RUŠKUC
R. GRAY
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, England e-mail: Robert.D.Gray@uea.ac.uk
V. MALTCEV
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, United Kingdom e-mail: victor@mcs.st-and.ac.uk, jamesm@mcs.st-and.ac.uk, nik@mcs.st-and.ac.uk
J. D. MITCHELL
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, United Kingdom e-mail: victor@mcs.st-and.ac.uk, jamesm@mcs.st-and.ac.uk, nik@mcs.st-and.ac.uk
N. RUŠKUC
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, United Kingdom e-mail: victor@mcs.st-and.ac.uk, jamesm@mcs.st-and.ac.uk, nik@mcs.st-and.ac.uk
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Abstract

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In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroups with finite Rees or Green index. Specific properties under consideration include stability, $\mathcal{D}=\mathcal{J}$ and minimal conditions on ideals.

Keywords

20M0520M12

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 1 , January 2014, pp. 65 - 86
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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