Rees Matrix Covers and the Translational Hull of a Locally Inverse Semigroup

Abstract

For any locally inverse semigroup S, there exists a maximal dense ideal extension of S within the class LI of all locally inverse semigroups (Pastijn and Oliveira, 2006, Preprint). Here we realize this maximal dense ideal extension in terms of a canonically constructed quotient of a regular Rees matrix semigroup over an inverse semigroup.

Key Words:

• Completely 0-simple semigroup
• Dense ideal extension
• Inverse semigroup
• Locally inverse semigroup
• Normal band of groups
• Order ideal
• Pseudosemilattice
• Rees matrix semigroup
• Thread
• Translational hull

2000 Mathematics Subject Classification:

• Primary 20M12, 20M17, 20M10
• Secondary 20M18

ACKNOWLEDGMENT

The second author was partially supported by FCT through Centro de Matemática da Universidade do Porto.

Notes

Communicated by V. Gould.