In this article, we construct some MDS quantum error-correcting codes (QECCs) from classes of constacyclic codes over $R_{s}=\mathbb F_{p}+u_{1}\mathbb F_{p}+ {\dots }+u_{s}\mathbb F_{p}$ , $u_{i}^{2}=u_{i}$ , $u_{i}u_{j}=u_{j}u_{i}=0$ , for odd prime $p$ and $i,j=1,2, {\dots },s,i\neq j$ . Many QECCs with improved parameters than the existing ones in some of the earlier papers are provided. We present a set of idempotent generators of the ring $R_{s}$ , and using that we define linear codes, determine all units, and study constacyclic codes over this ring. Among others, we study dual containing constacyclic codes over $R_{s}$ and construct (non-binary) QECCs. An algorithm to construct QECCs from dual containing constacyclic codes over $R_{s}$ is obtained that can provide many quantum codes.