  In this article we consider the exterior power and the symmetric tensors of
the polynomial ring in one variable. The structure of an associative semigraded
algebra of this polynomial ring induces on the symmetric tensors the structure
of an associative semigraded algebra, and on the exterior power induces
structure of a semigraded module over semigraded algebra of symmetric tensors.
The algebra of symmetric polynomials is isomorphic to the algebra of the
symmetric tensors of polynomial ring in one variables. We obtained the explicit
expression for symmetric polynomials via elementary symmetric polynomials and
the explicit expression for elements of the exterior power via elementary
symmetric polynomials and elements of the exterior power of the lower
polynomial degree.
