On idempotents and local property of $\Lambda \otimes_R R_{\mathfrak p}$ where $\Lambda$ is module finite algebra over commutative local ring $R$

Question

Let $R$ be a commutative Noetherian local ring. Let $\Lambda$ be a module finite associative $R$-algebra. Let $\mathfrak p$ be a prime ideal of $R$. I have the following two questions:

(1) If $\Lambda$ has no non-trivial idempotent elements, then does $\Lambda \otimes_R R_{\mathfrak p}$ have no non-trivial idempotent element?

(2) If $\Lambda$ has a unique maximal left ideal, then does $\Lambda \otimes_R R_{\mathfrak p}$ have a unique maximal left ideal ?