The group of units of a~free product of rings
    
    
  
  
  
      
      
      
        
Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 41-63
    
  
  
  
  
  
    
      
      
        
      
      
      
    Voir la notice de l'article provenant de la source Math-Net.Ru
            
              			The main theorem asserts that the multiplicative group of a free product of rings, all of which satisfy the condition $xy=1\Rightarrow yx=1$, with the amalgamated skew field $\Lambda$, is a free product of a certain family of its subgroups with an amalgamated subgroup $\Lambda\setminus\{0\}$. As an application a ring $R$ is indicated for which the group $\operatorname{GE}_n(R)$ is a nontrivial free factor of $\operatorname{GL}_n(R)$ ($n$ being any natural number greater than one). 
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      @article{SM_1989_62_1_a2,
     author = {V. N. Gerasimov},
     title = {The group of units of a~free product of rings},
     journal = {Sbornik. Mathematics},
     pages = {41--63},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_62_1_a2/}
}
                      
                      
                    V. N. Gerasimov. The group of units of a~free product of rings. Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 41-63. http://geodesic.mathdoc.fr/item/SM_1989_62_1_a2/
