This paper shows division rings are centrally algebraically closed, indicating a key algebraic property.
We introduce the concept of centrally algebraically closed division rings and show that a division ring satisfies the central Nullstellensatz if and only if it is centrally algebraically closed. We also show that every division ring can be embedded in a centrally algebraically closed division ring.
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Masood Aryapoor (2025) studied this question.
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