We define the spherical non-commutative torus

/ as the crossed product obtained by an iteration of l crossed products by actions of, the first action on C(

). Assume the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus

with a matrix algebra

( ) (m > 1). We prove that

/

(C) is not isomorphic to C(Prim(

/))

(C), and that the tensor product of

/ with a UHF-algebra

of type

is isomorphic to C(Prim(

/))

(C)

if and only if the set of prime factors of m is a subset of the set of prime factors of p. Furthermore, it is shown that the tensor product of

/, with the C＊-algebra K(H) of compact operators on a separable Hilbert space H is not isomorphic to C(Prim(

/))

(C) K(H) if Prim(

/) is homeomorphic to

(n)

for k and l' non-negative integers (k > 1), where

(n) is the lens space.

for k and l' non-negative integers (k > 1), where

(n) is the lens space.e.