Mathematics · Abstract Algebra
Which of the following statements is NOT correct for a Ring R with unity?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If e is an idempotent element, then exe - ex is a nilpotent element for all x in R.
- 2An element e in a ring R is idempotent if e2 = e.
- 3Both 0 and 1 are always nilpotent elements in any non-zero ring R.✓
- 4An element x in a ring R is nilpotent if xn = 0 for some positive integer n.
Correct answer
Both 0 and 1 are always nilpotent elements in any non-zero ring R.
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