Abstract
We extend some major theorems in commutative algebra to the class of modules that are not necessarily finitely generated. The novelty of our extension is that the hypothesis of finite generation over $R$ is replaced by one over $S$, where $R$ and $S$ are commutative Noetherian local rings and there is a local homomorphism $\varphi:R \rightarrow S$. Among the results that we extend are: Intersection Theorem and Intersection dimension formula.
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