On the Maximal Subsemigroups of the Increasing Order - Preserving Finite Transformation Semigroup
by
Kalcho Todorov
South-West University
Coauthors: Iliya Gyudhenov

We denoted by T_n the semigroup of all full transformations \alpha of the set X  =   { 1,   2,   ... ,   n },  by D_k  =  J_k  = {\alpha in T_n | |\alpha| =  k } the J_k-class- and by I_k  =  \cup _i=1^i=kJ_i the ideal of the semigroup T_n.
In this paper we consider the finite set X( < )  =  { 1 < 2 <   ...   < n } ordered in the standard way. We call a full transformation \alpha of X( < ) increasing order-preserving if i < j impies i\alpha < j\alpha &   i <= i\alpha. We describe the maximal subsemigroups of the J_k-classes and the I_k,   1 <= k <= n - 1 ideals of the semigroup of all increasing order-preserving transformations ot the set X( < ).

Date received: February 8, 2002