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Other Assets - Narrative (Details) - USD ($)
12 Months Ended
Jul. 31, 2022
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Goodwill [Line Items]        
Goodwill   $ 179,976,000 $ 171,601,000 $ 172,404,000
Goodwill impairment, result of annual impairment analysis $ 0      
Amortization of intangible assets   6,800,000 6,900,000 7,300,000
Ag        
Goodwill [Line Items]        
Goodwill   159,944,000 $ 160,475,000 $ 161,278,000
Nitrogen Production        
Goodwill [Line Items]        
Goodwill   $ 0    
Minimum | Other Intangible Assets        
Goodwill [Line Items]        
Intangible asset useful lives   2 years    
Maximum | Other Intangible Assets        
Goodwill [Line Items]        
Intangible asset useful lives   30 years