Let k(n) denote the connected nth Morava K-theory for the odd prime p and let k(n)\({}_*=\{\underline{k(n)}_ q\}\) be the associated \(\Omega\)-spectrum. Each \(H_*\underline{k(n)}_ q\) is a Hopf algebra and \(H_*\underline{k(n)}_*=\{H_*\underline{k(n)}_ q\}\) is a Hopf ring, where \(H_*\) stands for \(H_*(-;{\mathbb{Z}}/p).\) Using techniques of W. S. Wilson [Publ. Res. Inst. Math. Sci. 20, 1025-1036 (1984; Zbl 0564.55004)] and the bar spectral sequence, the author computes \(H_*\underline{k(n)}_*\). The second part of the paper contains a computation of the Hopf ring \(H_*\underline{bu}_*\).