  We study the structure of ideals generated by some classes of 2 \times 2
permanents of hypermatrices. This generalizes [9] on 2 x 2 permanental ideal of
generic matrices. We compare the obtained structure to that of the
corresponding determinantal ideals in [Swanson-Taylor 11]: while the notion of
t-switchability introduced in [11] plays a role for both permanental and
determinantal ideals, the permanents require further restrictions, which in
general increases the number of minimal primes. In the last two section we
examine a few related classes of permanental ideals.
  This is an extension of the first author's senior thesis at Reed College,
2011, under the second author's supervision.
