Geodesic
Axiomatic definition of a~quotient ring
Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 255-262.

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The quotient ring $Q\Phi(R)$ of the ring $R$ with respect to a strong filter $\Phi$ of right ideals of $R$ is axiomatically defined as a maximal strong $\Phi$-essential extension of $R$. The ring $Q\Phi(R)$ is constructively obtained in the form of $\lim\operatorname{Hom_r}(I,R)$, where $I\in\Phi$. 
@article{MZM_1974_15_2_a10,
     author = {V. P. Elizarov},
     title = {Axiomatic definition of a~quotient ring},
     journal = {Matemati\v{c}eskie zametki},
     pages = {255--262},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a10/}
}
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V. P. Elizarov. Axiomatic definition of a~quotient ring. Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 255-262. http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a10/