1. Math
  2. Advanced Math
  3. 1 let r be a ring a prove that if...

Question: 1 let r be a ring a prove that if...

Question details

1. Let R be a ring. (a) Prove that if R contains two elements i and j such that ir-: ris r and jr :-rj-r, for all r E R, then R is unital and i-: j -1R. (b) Suppose R is unital. Let r be an element of R, and suppose there exist elements u and v of R such that ur rU1R. Prove that u-v is the multiplicative inverse of r in R. (c) Let e be an element of R such that e? e. We say that e is an idempotent of R. Prove that the only idempotents of Z are 0 and 1.
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution