Construction of polynomial superalgebras (Q807734)

Let A be a finite-dimensional associative and commutative polynomial algebra over the complex field defined by an initial basis and equation. The author constructs another basis of the algebra A (standard basis) with convenient multiplication rule and indicates the formulae of transformations into the initial basis of A. The author shows that the algebra A possesses the structure of \({\mathbb{Z}}_ 2\)-graded space and gives some applications of his results.