On the maximal subsemigroups of the finite transformation semigropup
by
K. Todorov
South-West University, Blagoevgrad, Bulgaria
Coauthors: Iliya Gyudzhenov

The full transformation \alpha of X( < ) is isotone if i <= j   ===> i\alpha <= j\alpha; the full transformation \alpha of the set X( < ) is increasing isotone if for every i <= j   ===> i\alpha <= j\alpha& i <= i\alpha. We give a description of the maximal subsemigroups of all J'_k.  1 <= k <= n-1-classes and of all ideals I'_k of the semigroup of all increasing isotone transformations of a finite linearly ordered set X. The obtained results are based on previously proved propositions stating that elements of every J'_k-class, and therefore of every ideal I'_k, can be represented as products of idempotents of the same J'_k-class.

Date received: December 10, 2002