Definition:Integral Closure
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Definition
Let $R \subseteq A$ be an extension of commutative rings with unity.
"An extension" or "extensions"? Are both extensions (in which case "extensions") or is only $A$ an extension (in which case "commutative rings with unity" needs to be singular? As it stands the grammar is confusing.
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Let $C$ be the set of all elements of $A$ that are integral over $R$.
Then $C$ is called the integral closure of $R$ in $A$.
