We study central extensions of division rings with orderings of higher level. We show that orderings extend to certain immediate and inert extensions. Further, it is proved that any n–ordered division ring can be extended to a n–ordered division ring with almost real closed center. In the last section an old theorem due to Neumann is generalized: every n–ordered division ring can be extended to...

In this work we extend results introduced in [15]. Especially, we solve the reversibility problem for DNA codes over the non chain ring Rk,s = F42k [u1, . . . , us]/〈u 2 1 − u1, . . . , u 2 s − us〉. We define an automorphism θ over Rk,s which helps us both finding the idempotent decomposition of Rk,s and solving the reversibility problem via skew cyclic codes. Moreover, we introduce a generaliz...