  Using an approach to the Jacobian Conjecture by L.M. Dru\.zkowski and K.
Rusek 12], G. Gorni and G. Zampieri [19], and A.V. Yagzhev[27], we describe a
correspondence between finite dimensional symmetric algebras and homogeneous
tuples of elements of polynomial algebras. We show that this correspondence
closely relates Albert's problem [10, Problem 1.1], in classical ring theory
and the homogeneous dependence problem [13, page 145, Problem 7.1.5], in affine
algebraic geometry related to the Jacobian Conjecture. We demonstrate these
relations in concrete examples and formulate some open questions.
