Abundant Semigroups with a Multiplicative Adequate Transversal
Bai Liyan · Journal of Yuxi Normal University · 2009
The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal.We give a structure of dual-pair of this semigroup.It derives from the conclusion of a regular semigroup with an inverse transversal.The main theorem is that if S0 is an adequate semigroup,E0 is the idempotent set of S0,I is a left normal band with a multiplicative adequate transversal E0,L is an abundant semigroup with a multiplicative adequate transversal S0 whose idempotents form a right normal band,we define a new operation on the set I|×|L and can get I|×|L is an abundant semigroup whose multiplicative adequate transversal is isomorphic to S0.