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Acquisitions of Businesses - Schedule of Identifiable Intangible Assets Recorded in Conjunction with Acquisitions (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 31, 2016
Dec. 01, 2015
Oct. 28, 2015
Feb. 13, 2015
Jan. 31, 2016
Business Acquisition [Line Items]          
Fair Value         $ 2,577.7
Weighted average useful life (years)         14 years 2 months 12 days
OMG Malaysia          
Business Acquisition [Line Items]          
Fair Value $ 43.9        
Weighted average useful life (years) 14 years 3 months 18 days        
Alent          
Business Acquisition [Line Items]          
Fair Value   $ 682.9      
Weighted average useful life (years)   13 years 2 months 12 days      
Indefinite-lived trade names   $ 81.4      
OMG          
Business Acquisition [Line Items]          
Fair Value     $ 77.9    
Weighted average useful life (years)     19 years    
Arysta          
Business Acquisition [Line Items]          
Fair Value       $ 1,773.0  
Weighted average useful life (years)       14 years 3 months 18 days  
Customer lists          
Business Acquisition [Line Items]          
Fair Value         $ 751.4
Weighted average useful life (years)         19 years 1 month 6 days
Customer lists | OMG Malaysia          
Business Acquisition [Line Items]          
Fair Value $ 41.0        
Weighted average useful life (years) 15 years        
Customer lists | Alent          
Business Acquisition [Line Items]          
Fair Value   $ 391.4      
Weighted average useful life (years)   14 years 8 months 12 days      
Customer lists | OMG          
Business Acquisition [Line Items]          
Fair Value     $ 49.0    
Weighted average useful life (years)     24 years 3 months 18 days    
Customer lists | Arysta          
Business Acquisition [Line Items]          
Fair Value       $ 270.0  
Weighted average useful life (years)       25 years  
Developed technology          
Business Acquisition [Line Items]          
Fair Value         $ 1,484.2
Weighted average useful life (years)         11 years 8 months 12 days
Developed technology | OMG Malaysia          
Business Acquisition [Line Items]          
Fair Value $ 2.9        
Weighted average useful life (years) 5 years        
Developed technology | Alent          
Business Acquisition [Line Items]          
Fair Value   $ 203.3      
Weighted average useful life (years)   10 years      
Developed technology | OMG          
Business Acquisition [Line Items]          
Fair Value     $ 28.0    
Weighted average useful life (years)     10 years    
Developed technology | Arysta          
Business Acquisition [Line Items]          
Fair Value       $ 1,250.0  
Weighted average useful life (years)       12 years  
Tradenames          
Business Acquisition [Line Items]          
Fair Value         $ 339.7
Weighted average useful life (years)         18 years 3 months 18 days
Tradenames | OMG Malaysia          
Business Acquisition [Line Items]          
Fair Value $ 0.0        
Tradenames | Alent          
Business Acquisition [Line Items]          
Fair Value   $ 85.8      
Weighted average useful life (years)   20 years      
Tradenames | OMG          
Business Acquisition [Line Items]          
Fair Value     $ 0.9    
Weighted average useful life (years)     10 years    
Tradenames | Arysta          
Business Acquisition [Line Items]          
Fair Value       $ 253.0  
In Process Research and Development          
Business Acquisition [Line Items]          
In process - research and development         $ 2.4
In Process Research and Development | OMG Malaysia          
Business Acquisition [Line Items]          
In process - research and development $ 0.0        
In Process Research and Development | Alent          
Business Acquisition [Line Items]          
In process - research and development   $ 2.4      
In Process Research and Development | OMG          
Business Acquisition [Line Items]          
In process - research and development     $ 0.0    
In Process Research and Development | Arysta          
Business Acquisition [Line Items]          
In process - research and development       $ 0.0