Geodesic
Maximal and minimal ideals of centrally essential rings
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 219 (2023), pp. 50-53

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We show that a ring $R$ with center $Z(R)$ such that the module $R_{Z(R)}$ is an essential extension of the module $Z(R)_{Z(R)}$ need not be right quasi-invariant, i.e., not all maximal right ideals of the ring $R$ are ideals. In terms of the central essentiality property, we obtain sufficient conditions for the fact that all maximal right ideals are ideals.
Keywords: centrally essential ring, maximal right ideal, minimal right ideal. 
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     author = {O. V. Ljubimtsev and A. Tuganbaev},
     title = {Maximal and minimal ideals of centrally essential rings},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {50--53},
     publisher = {mathdoc},
     volume = {219},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_219_a4/}
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O. V. Ljubimtsev; A. Tuganbaev. Maximal and minimal ideals of centrally essential rings. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 219 (2023), pp. 50-53. http://geodesic.mathdoc.fr/item/INTO_2023_219_a4/