On the fundamental double four-spiral semigroup
Pierre Antoine Grillet · Bulletin of the Belgian Mathematical Society - Simon Stevin · 1996
We give a new description of the fundamental double four-spiral semigroup. The fundamental four-spiral semigroup Sp4 and the fundamental double fourspiral semigroup DSp4 were introduced in [1], [3], and [4]. These semigroups are interesting examples of fundamental regular semigroups, and are indispensable building blocks of bisimple, idempotent-generated regular semigroups. Their basic properties are recalled in parts 1 and 2 of this note. In part 3 we give an alternate construction ofDSp4 in terms of the free semigroup on two generators, as a set of quadruples with a simple, bicyclic-like multiplication. This permits shorter proofs and easier access to the main properties of DSp4 :d escriptions of DSp4=L and DSp4=R (part 4); reduced form of the elements (part 5); and the property of congruencesC6Lthat DSp4=C is completely simple (part 6).