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- Jun 22, 2012

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In Chapter 3: Prime Ideals and Maximal Ideals, Exercise 3.19 reads as follows:

Let R be a quasi-local commutative ring with maximal ideal M.

Show that the ring \(\displaystyle R[[X_1, ... \ ... , X_n]] \) of formal power series in indeterminates \(\displaystyle X_1, ... \ ... , X_n \) with coefficients in R is again a quasi-local ring, and that its maximal ideal is generated by \(\displaystyle M \cup \{ X_1, ... \ ... , X_n \} \)

**Can someone please help me get started on this problem?**

Peter

Note: On page 41, Chapter 3, Sharp defines a quasi-local ring as follows:

3.12 Definition. A commutative ring R which has exactly one maximal ideal, M say, is said to be quasi-local.