Geodesic
Associative rings with large center
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 141-144.

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A ring $R$ is called a ring with large center if any nonzero ideal of $R$ has nonzero intersection with the center of $R$. We give some conditions for an ideal of a ring with large center to be itself a ring with large center, and also we provide an example of a ring with large center $R$ and its ideal $I\lhd R$ such that $I$ is not a ring with large center. 
@article{FPM_2012_17_4_a7,
     author = {D. V. Zlydnev},
     title = {Associative rings with large center},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {141--144},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a7/}
}
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D. V. Zlydnev. Associative rings with large center. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 141-144. http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a7/

[1] Armendariz E. P., Birkenmeier G. F., Park J. K., “Ideal intrinsic extensions with connections to PI-rings”, J. Pure Appl. Algebra, 213 (2009), 1756–1776 | DOI | MR | Zbl