Hi guys. You know that a vector space V is a set with two operations + and * that satisfy the following properties. However last statement seems to be too obvious (1*u = u) so: Is there a space which satisfies with the first 9 statements and it doesn't satifies the last one (1 * u = u). Thanks or your help!

1)f u and v are elements of V, then u + v is and element of V (closure under +)

2) u + v = v + u

3) u + (v + w) = (u + v) + w

4) There is an element 0 in V such that

u + 0 = 0 + u = u

5) For every u in V there is an element -u with

u + (-u) = 0

6) If u is in V and c is a real number then c*u is in V (closure under *)

7) c * (u + v) = c * u + c * v

8 ) (c + d) * u = c * u + d * u

9 ) c * (d * u) = (cd) * u

10) 1 * u = u