Mathematics 894 Problem Set 3

Suggested reading: Section 10.4, noting especially the examples on pages 366-367, and the proof of Proposition 21, page 374.

Solutions due next week (Friday February 1).

1. Page 375: #3, 4, 6.

2. Page 376: #11. Also write e_{1} ⊗ e_{1} + e_{2} ⊗ e_{1} − 2e_{1} ⊗ e_{2} − 2e_{2} ⊗ e_{2} as a simple tensor v ⊗ w.

3. Page 377: #18.

4. Page 377: Verify that the multiplication in Proposition 21, page 374, makes A ⊗_{R} B into an R-algebra. What is R[X] ⊗_{R} R[X]?