Embedding Into Almost Left Factorizable Restriction Semigroups

Abstract

The notion of almost left factorizability and the results on almost left factorizable weakly ample semigroups, due to Gomes and the author, are adapted for restriction semigroups. The main result of the paper is that each restriction semigroup is embeddable into an almost left factorizable restriction semigroup. This generalizes a fundamental result of the structure theory of inverse semigroups.

Key Words:

• Almost left factorizability
• Restriction semigroup
• W-product
• Weakly E-ample semigroup

2000 Mathematics Subject Classification:

• 20M10
• 20M05

ACKNOWLEDGMENT

Research supported by the Hungarian National Foundation for Scientific Research grant no. SAB81142.

Notes

The empty set is not considered an order ideal.

Communicated by V. Gould.