A characterization of $F$-algebras with all one-sided ideals closed
Volume 168 / 2005
                    
                    
                        Studia Mathematica 168 (2005), 135-145                    
                                        
                        MSC: 46H10, 13E05.                    
                                        
                        DOI: 10.4064/sm168-2-4                    
                                    
                                                Abstract
We prove that a real or complex $F$-algebra has all left and right ideals closed if and only if it is noetherian.
 
             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                         
                                                            