Geodesic
Centrally essential rings which are not necessarily unital or associative
Diskretnaya Matematika, Tome 30 (2018) no. 4, pp. 42-47

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Centrally essential rings were defined earlier for associative unital rings; in this paper, we define them for rings which are not necessarily associative or unital. In this case, it is proved that centrally essential semiprime rings are commutative. It is proved that all idempotents of a centrally essential alternative ring are central. Several examples of non-commutative centrally essential rings are provided, some properties of centrally essential rings are described.
Keywords: centrally essential ring, semiprime ring, idempotent, non-unital ring, alternative ring. 
@article{DM_2018_30_4_a3,
     author = {V. T. Markov and A. A. Tuganbaev},
     title = {Centrally essential rings which are not necessarily unital or associative},
     journal = {Diskretnaya Matematika},
     pages = {42--47},
     publisher = {mathdoc},
     volume = {30},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_4_a3/}
}
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V. T. Markov; A. A. Tuganbaev. Centrally essential rings which are not necessarily unital or associative. Diskretnaya Matematika, Tome 30 (2018) no. 4, pp. 42-47. http://geodesic.mathdoc.fr/item/DM_2018_30_4_a3/