Unique Constrution of Formanek Central Polynomial
Received:November 21, 1988  
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Zheng Yumei Department of Mathematics
Hubei University 
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Abstract:
      Formanek constructed the first central polynomial. i .e. G1 G2 … Gn where G1= G(x, y1,…, yn), G2= G(x, y2, y3,…, yn, y1) etc. Are called Forma nek's polynomials. Rosset in his nota [3] raised the question that whether all sgmmetic polynomials in Gi also give central polynomials. He showed that the basic sgmmetric polynomials in Gi are not all central. In this paper we shall show, for n≥3 each polynomial in Gj is not central, except f(G1 … Gn, where f(x)is a polynomial at x. Hence Formanek's central polynomial is unique in some sense.
Citation:
DOI:10.3770/j.issn:1000-341X.1990.02.004
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