On set theoretically and cohomologically complete intersection ideals

Let $(R,\text{fm})$ be a local ring and $\text{fa}$ be an ideal of $R$. The inequalities $$\begin{array}{l}\text{Ht}(\text{fa})\le \text{cd}(\text{fa},R)\le \text{ara}(\text{fa})\le l(\text{fa})\le \mu (\text{fa})\end{array}$$ are known. It is an interesting and long-standing problem to find out the cases giving equality. Thanks to the formal grade we give conditions in which the above inequalities become equalities.