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In this article we show that the coordinates of a period lattice generator ofthe $n$-th tensor power of the Carlitz module are algebraically independent, if$n$ is prime to the characteristic. The main part of the paper, however, isdevoted to a general construction for $t$-motives which we call prolongation,and which gives the necessary background for our proof of the algebraicindependence. Another ingredient is a theorem which shows hypertranscendencefor the Anderson-Thakur function $\omega(t)$, i.e. that $\omega(t)$ and all itshyperderivatives with respect to $t$ are algebraically independent.

Prolongations of t-motives and algebraic independence of periods