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 $z_1z_2 \cdots z_n=z_{i_1}z_{i_2}\cdots z_{i_n}~ (n\geq2)$ with $i_n \neq n ~~[i_1 \neq 1]$ 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 $S$.
Alam, R., Ashraf, W., & Khan, N. (2024). On closedness of some permutative posemigroup identities. Journal of Algebra and Related Topics, 12(1), 1-12. doi: 10.22124/jart.2023.23645.1498
MLA
R. Alam; W. Ashraf; N. Mohammad Khan. "On closedness of some permutative posemigroup identities". Journal of Algebra and Related Topics, 12, 1, 2024, 1-12. doi: 10.22124/jart.2023.23645.1498
HARVARD
Alam, R., Ashraf, W., Khan, N. (2024). 'On closedness of some permutative posemigroup identities', Journal of Algebra and Related Topics, 12(1), pp. 1-12. doi: 10.22124/jart.2023.23645.1498
VANCOUVER
Alam, R., Ashraf, W., Khan, N. On closedness of some permutative posemigroup identities. Journal of Algebra and Related Topics, 2024; 12(1): 1-12. doi: 10.22124/jart.2023.23645.1498
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