Ma, Jingjing2020-09-032020-09-032016Ma, J., Wu, L. & Zhang, Y. Directed Partial Orders on Complex Numbers and Quaternions over Non-Archimedean Linearly Ordered Fields. Order 34, 37–44 (2017).https://hdl.handle.net/10657.1/2444Let 'F' be a non-archimedean linearly ordered field, and 'C' and 'H' be the field of complex numbers and the division algebra of quaternions over 'F', respectively. In this paper, a class of directed partial orders on 'C' are constructed directly and concretely using additive subgroup of 'F+'. This class of directed partial orders includes those given in Rump and Wang (J. Algebra 400, 1-7, 2014), and Yang (J. Algebra 295 (2), 452-457, 2006) as special cases and we conjecture that it covers all directed partial orders on 'C' such that 1>0. It turns out that this construction also works very well on 'H'. We note that none of these directed partial orders is a lattice order on 'C' or 'H'.Non-archimedean linear ordered field, Directed partially ordered algebra, Directed partial order, Admissible semigroup, Lattice orderArticle