In 1984, A. Restivo and C. Reutenauer solved the Burnside problem for semigroups. They proved that a finitely generated semigroup is finite if and only if it is periodic and has the permutation property P n for some integer n ≥ 2. This fact drown the attention to semigroups satisfying some permutation properties. The semigroups satisfying the permutation property P 2 are exactly the commutative semigroups. All of semigroups considered in this book are generalized commutative semigroups and most of them have some permutation property. In their examinations the commutative semigroups are appeared in subcases. That is why we deal with them in a separated chapter. The literature of commutative semigroups is very rich, but we present only those results which will be used in the other chapters of this book.
KeywordsCommutative Semigroup Idempotent Element Ideal Extension Cancellative Semigroup Nontrivial Subgroup
Unable to display preview. Download preview PDF.