Geodesic
Linearly ordered rings which are not $o$-epimorphic images of ordered free rings
Matematičeskie zametki, Tome 9 (1971) no. 6, pp. 693-697

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A proof is given that not every linearly ordered associative (associative-commutative) ring is the $o$-image of a free associative (associative-commutative) ring for some ordering of the latter. There are also nilpotent linearly ordered rings which are not $o$-epimorphic images of free associative or free associative-commutative $n$-nilpotent rings for $n\ge4$, no matter what ordering is used for the latter. 
@article{MZM_1971_9_6_a9,
     author = {O. A. Ivanova},
     title = {Linearly ordered rings which are not $o$-epimorphic images of ordered free rings},
     journal = {Matemati\v{c}eskie zametki},
     pages = {693--697},
     publisher = {mathdoc},
     volume = {9},
     number = {6},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a9/}
}
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O. A. Ivanova. Linearly ordered rings which are not $o$-epimorphic images of ordered free rings. Matematičeskie zametki, Tome 9 (1971) no. 6, pp. 693-697. http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a9/