Kaplansky's conjectures refer to a set of conjectures proposed by the mathematician David Kaplansky, primarily in the area of ring theory and algebra. One of the most famous is related to the structure of rings, particularly concerning division rings and their fields of fractions. 1. **Kaplansky's Division Ring Conjecture**: This conjecture posits that every division ring that is finitely generated as a module over its center is a field.
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