Author:
Sareeto Apatsara,Koppitz Jörg
Abstract
AbstractWe study a submonoid of the well studied monoid $$POI_n$$
P
O
I
n
of all order-preserving partial injections on an n-element chain. The set $$IOF_n^{par}$$
I
O
F
n
par
of all partial transformations in $$POI_n$$
P
O
I
n
which are fence-preserving as well as parity-preserving forms a submonoid of $$POI_n$$
P
O
I
n
. We describe Green’s relations and ideals of $$IOF_n^{par}$$
I
O
F
n
par
. For each ideal of $$IOF_n^{par}$$
I
O
F
n
par
, we characterize the maximal subsemigroups. We observe that there are three different types of maximal subsemigroups.
Publisher
Springer Science and Business Media LLC