ok here is a 6 dim candidate
(very similar to dimension 5 posted earlier. The squaring formula is also the same up to 3 trivial sign changes)
the coefficients are reals.
the units are defined as :
a^2 = b^2 = 1.
c^2 = d^2 = e^2 = -1.
a b = c
a c = d
a d = e
a e = b
b c = e
b d = a
b e = d
c d = b
c e = a
d e = c
som and products are commutative.
som and product behave distributive.
i was not able to find nonzero numbers w such that w^2 = 0.
I assume no such nonzero w exist.
regards
tommy1729
(very similar to dimension 5 posted earlier. The squaring formula is also the same up to 3 trivial sign changes)
the coefficients are reals.
the units are defined as :
a^2 = b^2 = 1.
c^2 = d^2 = e^2 = -1.
a b = c
a c = d
a d = e
a e = b
b c = e
b d = a
b e = d
c d = b
c e = a
d e = c
som and products are commutative.
som and product behave distributive.
i was not able to find nonzero numbers w such that w^2 = 0.
I assume no such nonzero w exist.
regards
tommy1729