Hochschild cohomologies for $Z$-rings with a power basis

Let $\Lambda$ be an associative ring with unity. The main result of the article consists in the proof of the periodicity of the Hochschild cohomologies of $\Lambda$ in the case when $\Lambda$ is a $Z$-ring with a power basis. The period is equal to 2. This result is proved for maximal orders of fields of algebraic numbers.