Let $R$ be a (associative, commutative) local ring, denote by $\mathfrak{m}$ its maximal ideal. For any other ideal $J\subset R$ one can speak about:
- the biggest power $k\le\infty$ such that $J\subseteq\mathfrak{m}^k$
- the smallest power k such that $J\supseteq\mathfrak{m}^k$ (assuming $J$ contains some power of the maximal ideal)
What are the standard notations for these numbers? (for the first number I'd use $ord_{\mathfrak{m}}(J)$, but no idea about the second number)