On closedness of some permutative posemigroup identities

As we know that all non-trivial permutation identities  are not preserved under epimorphisms of partially ordered semigroups.  In this paper towards this open problem, first we show that certain non-trivial identities in conjunction with the permutation identity z_۱z_۲ \cdots z_n=z_{i_۱}z_{i_۲}\cdots z_{i_n}~   (n\geq۲) with i_n \neq n  ~~[i_۱ \neq ۱]  are preserved under epimorphisms of partially ordered semigroups. Further, we extend a result of Ahanger and Shah which showed that the center of a partially ordered semigroup S is closed in S and show that the normalizer of any element of a partially ordered semigroup S is closed in S.

کلیدواژه ها:

Posemigroups ، Dominion ، Zigzag ، variety