Ordered abundant semigroups with adequate transversals
Abdulsalam El-Qallali · Communications in Algebra · 2021
Abundant semigroups containing multiplicative ample transversals are introduced by the author. Guo establishes the structure of abundant semigroups with multiplicative adequate transversals. As any ample semigroup is adequate, is Guo’s structure an extension of that introduced by the author? After answering this question positively and providing a natural order for the multiplicative ample transversal case, an order analogue of Guo’s structure is also demonstrated. Since left normal bands and right normal bands, each with a skeleton, play a vital role in establishing the structure of the classes of abundant semigroups under consideration, some attention has been paid to the structure of such bands.