Please see an attachment for details Image transcription textExercise 8. Let

  

Please see an attachment for details Image transcription textExercise 8. Let R be a commutative ring. An element :1: E R is called nilpotent if there exists a positive m E Zsuch that 33′” = 0. (a) Show that I = {m E R : x is nilpotent} is an ideal of R (called the radical of R). Hint:the usual binomial theorem (3 + y)” = 22:0 (Z)xky”—k holds for all at, y E R. (b) Show th… …   Math Algebra MATH 541 Share (0)