Multiple choice questions on commutative algebra Ali Akbar Alijani Department of Mathematics, University of Guilan e-mail: aliakbaralijani@yahoo.com Hossein Sahleh Department of Mathematics, University of Guilan e-mail: sahleh@guilan.ac.ir In all questions, R is a commutative ring with identity. Question 1. Let M be a f.g. R−module with only one maximal submod- ule. Which of the following statements is true? 1. M is noetherian. 2. every submodule of M is cyclic. 3. M is cyclic. 4. R is a PID. Question 2. Which of the following statements is true? 1. every artinian ring is noetherian. 2. every artinian module is noetherian. 3. in a noetherian ring, every prime ideal is maximal. 4. every noetherian ring is artinian. 1