sentences:  Specifically, it is the restriction to 
  formula_4 of the (linear) projection from formula_5 to formula_6 whose
  kernel is spanned by the elements of "G" outside formula_3.The image of this map is contained in 
  formula_8, and it transpires that the map is also a ring homomorphism.Since it is a ring homomorphism, for any block "B" of "FG", the Brauer homomorphism 
  sends the identity element of "B" either to "0" or to an idempotent element.