Let X be a projective smooth variety over a field k. In the first part we show that an indecomposable element in CH
2(X, 1) can be lifted to an indecomposable element in CH
, 2) where K is the function field of 1 variable over k. We also show that if X is the self-product of an elliptic curve over ℚ then the ℚ-vector space of indecomposable cycles is infinite dimensional.
In the second part we give a new definition of the group of indecomposable cycles of CH
3(X, 2) and give an example of non-torsion cycle in this group.