(a) Show that a ring has only one zero element. [Hint: If there were more than...

 

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(a) Show that a ring has only one zero element. [Hint: If there were more than one, how many solutions would the equation OR+ x = 0Rhave?] (b) Show that a ring Rwith identity has only one identity element. (c) Can a unit in a ring Rwith identity have more than one inverse? Why? (a) Show that a ring has only one zero element. [Hint: If there were more than one, how many solutions would the equation OR+ x = 0Rhave?] (b) Show that a ring Rwith identity has only one identity element. (c) Can a unit in a ring Rwith identity have more than one inverse? Why?

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