Rational Solver
+1 vote
149 views
Let $\mathrm{R}$ be a commutative ring with unity. Which of the following is true?

1. If $\mathrm{R}$ has finitely many prime ideals, then $\mathrm{R}$ is a field

2. If $R$ has finitely many ideals, then $R$ is finite

3. If $R$ is a P.I.D., then every subring of $R$ with unity is a P.I.D.

4. If $\mathrm{R}$ is an integral domain which has finitely many ideals, then $\mathrm{R}$ is a field
in Abstract Algebra by Expert | 149 views

Please log in or register to answer this question.

Welcome to Rational Solver, where you can ask questions and receive answers from other members of the community.
66 questions
23 answers
2 comments
1,801 users