On Relative Ranks of the Semigroup of Orientation-preserving Transformations on Infinite Chains

Abstract

In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations.

On relative ranks of the semigroup of orientation-preserving transformations on infinite chains

“…Clearly, O(X) ⊆ OP(X) and we have α ∈ O(X) if and only if α ∈ OP(X) and α admits X as an ideal. In [5], Dimitrova and Koppitz determined the relative rank of the semigroup OP(X) modulo O(X) for some infinite chains X.…”

“…The relative generating sets of OP(X) modulo O(X) of minimal sizeIn[5], Dimitrova and Koppitz determined the relative rank of the semigroup OP(X) modulo O(X) for certain infinite chains X. It remains a characterization of the relative generating sets of OP(X) modulo O(X) of minimal…”