EN
The generalized non-commutative torus $T_{ϱ}^{k}$ of rank n is defined by the crossed product $A_{m/k} ×_{α₃} ℤ ×_{α₄}... ×_{αₙ} ℤ$, where the actions $α_{i}$ of ℤ on the fibre $M_{k}(ℂ)$ of a rational rotation algebra $A_{m/k}$ are trivial, and $C*(kℤ × kℤ) ×_{α₃} ℤ ×_{α₄} ... ×_{αₙ} ℤ$ is a non-commutative torus $A_{ϱ}$. It is shown that $T^{k}_{ϱ}$ is strongly Morita equivalent to $A_{ϱ}$, and that $T_{ϱ}^{k} ⊗ M_{p^{∞}}$ is isomorphic to $A_{ϱ} ⊗ M_{k}(ℂ) ⊗ M_{p^{∞}}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p.