Mathematics · Abstract Algebra
Let R and S be non-zero commutative rings with multiplicative identities 1 R and 1 S , respectively. Let f: R → S be a ring homomorphism with f(1 R ) = 1 S . Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If a is a unit in R, then f(a) is a unit in S✓
- 2If R is a field, then f(a) is a unit in S for every non-zero element a ∈ R
- 3If f(a) is a unit in S for every non-zero element a ∈ R, then f(R) is a field
- 4If f(a) is a unit in S for every non-zero element a ∈ R, then S is a field
Correct answer
If a is a unit in R, then f(a) is a unit in S
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