Base fields of $\mathrm{csp}$-rings

We study into the question of which fields may serve as base fields for $\mathrm{csp}$-rings. It is proved that every algebraic extension of a field $\mathbf Q$ is the base field of some $\mathrm{csp}$-ring. Also it shown that in studying base fields, we may confine ourselves to treating only $\mathrm{csp}$-rings of idempotent cocharacteristic, or only regular $\mathrm{csp}$-rings.