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This failure of unique factorization in some cyclotomic fields led Ernst Kummer to the concept of ideal numbers and , later , Richard Dedekind to ideals .
 person: Ernst Kummer; person: Richard Dedekind
Given options, please tell me the categories of all the listed entity words.Output format is "type1: word1; type2: word2". 
Option: location, person, organization 
Text: {0} 
 Entities: Ernst Kummer, Richard Dedekind 
Answer:
 person: Ernst Kummer; person: Richard Dedekind