Let $R$ be a ring and $R'$ an overring of $R$. What does $[R':x]_R$ mean for $x \in R'$?
2026-04-04 20:56:34.1775336194
What does the notation $[R':x]_R$ mean in this context?
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It depends on the context. Because of your title it reminds me on the ideal quotient.
Definition: Let $I,J$ be ideals in a ring $R$. Then $$ (I:J)_R=(I:J)=\{a\in R\mid aJ\subseteq I\} $$ is the ideal quotient. Here $(I:x):=(I:(x))$, where $(x)$ is the principal ideal generated by $x$.