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\title{Math 724\\Summer 2009\\Homework 3}
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\centerline{\it Yesterday.}

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\noindent 1. (5 pt) Show that $\text{Tor}_n^R(A,B)$ is well-defined. That is, show that $\text{Tor}_n^R(-,B)$ acts on $A$ equivalently to the way that $\text{Tor}_n^R(A,-)$ acts on $B$.

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\noindent 2. (5 pt) Let $R$ be a domain. Show that if $I\subseteq R$ is an ideal then $I$ is a projective $R-$module, and use this to conclude that if $R$ is Dedekind then every ideal is projective.



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