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Commitments and Contingencies (Details Textual) - USD ($)
$ in Millions
3 Months Ended 12 Months Ended
Dec. 31, 2018
Dec. 31, 2019
Dec. 31, 2018
Dec. 31, 2017
Apr. 02, 2013
Business Acquisition [Line Items]          
Maximum contingent consideration in the form of development and approval milestones   $ 735.0      
Increase to goodwill   117.5 $ 1,080.1    
Potential future milestone payments commitment, approximately   6,800.0      
Cancellable future commitments   514.0      
Income Taxes Paid   87.0      
Commitments And Contingencies (Textual)          
Accrued expenses   24.0      
Liabilities associated with uncertain tax positions   136.9      
TYSABRI          
Business Acquisition [Line Items]          
Future contingent payment for annual worldwide net sales up to $2.0 billion         18.00%
Future contingent payment threshold         $ 2,000.0
Future contingent payment for annual worldwide net sales that exceed $2.0 billion         25.00%
Solothurn          
Business Acquisition [Line Items]          
Cancellable future commitments   52.0      
TECFIDERA | Fumapharm AG          
Business Acquisition [Line Items]          
Increase to goodwill $ 300.0   1,200.0    
Twenty billion | TECFIDERA | Fumapharm AG          
Business Acquisition [Line Items]          
Cumulative sales level 20,000.0   20,000.0    
Increase to goodwill 300.0        
Each additional one billion up to twenty billion | TECFIDERA | Fumapharm AG          
Business Acquisition [Line Items]          
Cumulative sales level $ 20,000.0   $ 20,000.0    
Development Milestones          
Business Acquisition [Line Items]          
Potential future milestone payments commitment, approximately   1,200.0      
Regulatory Milestones          
Business Acquisition [Line Items]          
Potential future milestone payments commitment, approximately   1,400.0      
Commercial Milestones [Member]          
Business Acquisition [Line Items]          
Potential future milestone payments commitment, approximately   4,200.0      
2017 Tax Act          
Business Acquisition [Line Items]          
Transition toll tax liabilities   $ 697.0   $ 989.6  
Ionis Pharmaceuticals | Minimum | SPINRAZA          
Business Acquisition [Line Items]          
Percentage Of Royalties As Per Collaboration   11.00%      
Ionis Pharmaceuticals | Maximum | SPINRAZA          
Business Acquisition [Line Items]          
Percentage Of Royalties As Per Collaboration   15.00%      
Alkermes          
Business Acquisition [Line Items]          
Potential future milestone payments commitment, approximately   $ 155.0      
Alkermes | VUMERITY          
Business Acquisition [Line Items]          
Percentage Of Royalties As Per Collaboration   15.00%      
Twelve months          
Business Acquisition [Line Items]          
Potential future milestone payments commitment, approximately   $ 430.0