**Problems in bold are to be handed in**

Unless noted otherwise, problems are from Dummit and Foote.

Chapter 8.2 / 6

Chapter 9.3 / 4

Chapter 9.4 / 16

**Hand in:**Let*R*be a unique factorization domain, and*S*a multiplicative subset of*R*not containing*0*. Show that*R[S*is also a unique factorization domain.^{-1}]**Hand in:**Let*R*be a commutative ring, and*S*a multiplicative subset of*R*. Exhibit a bijective correspondence between**prime**ideals of*R*disjoint from*S*, and ideals of*R[S*.^{-1}]