#TITLE_ALTERNATIVE# - Kurniadi (NIM : 20105007), Edi
abstrct: An algebra (A,.,+;k) over a field is a ring (A,.,+) endowed with an action of k on A which is compatible with both the multiplication and addition. Thus (A,.,+) is a ring, (A, +; k) is a vector space and myu(ab)=(myu a)b=a(myu b) for all a, b equifalent A and myu equifalent k. Tensor product will suggest to the algebra definition equivalently with the first definition above. The duality of this definition suggests to the concept of a coalgebra. This thesis shows that any algebra is the dual of coalgebra and the convers is true if the algebra dimension is finite.