Let be a ring in wich is the only nilpotent element ( ) . Prove that is invertible if and only if x is left invertible .
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Originally Posted by petter Let be a ring in which is the only nilpotent element ( ) . Prove that is invertible if and only if x is left invertible . Hint: Let be a left inverse for . Then is nilpotent (just check that its square is 0).
Originally Posted by Opalg Hint: Let be a left inverse for . Then is nilpotent (just check that its square is 0). So . How to continue ?
Originally Posted by petter So . How to continue ? Multiply on the left by .
Originally Posted by Opalg Multiply on the left by . I'm stupid . Thx !
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