This research describes centrally essential rings' structures through various extension types, highlighting their properties.
A non-zero unital ring R is said to be centrally essential if for every nonzero element a of R, there exist non-zero central elements x and y with ax = y. In the paper, almost fully prime centrally essential rings are described in terms of ideal extensions, centrally essential Dorroh extensions, and trivial extensions.
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Lyubimtsev et al. (2026) studied this question.
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