Geodesic
Moulton Affine Hjelmslev Planes
Canadian mathematical bulletin, Tome 21 (1978) no. 2, pp. 135-142

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Desarguesian affine Hjelmslev planes (D.A.H. planes) were introduced by Klingenberg in [1] and generalized by Lane and Lorimer in [2]. D.A.H. planes are coordinatized by affine Hjelmslev rings (A.H. rings) which are local rings whose radicals are equal to their sets of two-sided zero divisors and whose principal right ideals are totally ordered. In [5], ordered D.A.H. planes were defined and the induced orderings of their A.H. rings were discussed. In this note an ordered non-Desarguesian A.H. plane is constructed from an arbitrary ordered D.A.H. plane. The existence of such planes ensures that the discussion of ordered non-Desarguesian A.H. planes by J. Laxton in [3] is meaningful. The basic idea employed is essentially the same as the one used in the construction of the classical Moulton plane from the real affine plane (cf. [4]) 
Baker, Catharine. Moulton Affine Hjelmslev Planes. Canadian mathematical bulletin, Tome 21 (1978) no. 2, pp. 135-142. doi: 10.4153/CMB-1978-024-7
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     title = {Moulton {Affine} {Hjelmslev} {Planes}},
     journal = {Canadian mathematical bulletin},
     pages = {135--142},
     year = {1978},
     volume = {21},
     number = {2},
     doi = {10.4153/CMB-1978-024-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-024-7/}
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