42364
For associative algebra s , the definition can be simplified as follows : an associative algebra over a field is a division algebra if and only if it has a multiplicative identity element 1 ≠ 0 and every non-zero element a has a multiplicative inverse ( i.e. an element x with ax = xa = 1 ) .
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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:  
Answer:
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