Abundance of E-order-preserving transformation semigroups

作者：Sun, Lei^*; Han, Xuefeng

来源：Turkish Journal of Mathematics, 2016, 40(1): 32-37.

DOI：10.3906/mat-1412-37

• Transformation semigroup
• L*-relation
• R*-relation
• idempotent
• abundance

Let T-x be the full transformation semigroup on a finite totally ordered set X = {1 < 2 < ... < n} (n >= 3) and E be a nontrivial equivalence relation on X. In this paper, we consider a subsemigroup of T-X defined by
EOPX = {f is an element of T-X : x,y is an element of X, (x, y) is an element of E, x <= y -> (f (x), f (y)) is an element of E, f (x) <= f (y)}
and present a necessary and sufficient condition under which the semigroup EOPX is abundant.

• 出版日期2016
• 单位河南理工大学