Geodesic
Nonaxiomatizability of lattice-orderable rings
Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 449-452.

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Two elementarily equivalent rings, one of which is lattice-orderable and the other is not lattice-orderable, are constructed. Hence follows the elementary non closedness and the nonaxiomatizability of the class of all lattice-orderable rings. This example shows that the class of all lattice-orderable rings is nonaxiomatizable in the class of directedly orderable rings. 
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     author = {A. A. Vinogradov},
     title = {Nonaxiomatizability of lattice-orderable rings},
     journal = {Matemati\v{c}eskie zametki},
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     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a0/}
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A. A. Vinogradov. Nonaxiomatizability of lattice-orderable rings. Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 449-452. http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a0/