A Classification of Bisymmetric Polynomial Functions over Integral Domains of Characteristic Zero
نویسنده
چکیده
We describe the class of n-variable polynomial functions that satisfy Aczél’s bisymmetry property over an arbitrary integral domain of characteristic zero with identity.
منابع مشابه
HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC
Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...
متن کاملD-nice Symmetric Polynomials with Four Roots over Integral Domains D of Any Characteristic
Let D be any integral domain of any characteristic. A polynomial p(x) ∈ D[x] is D-nice if p(x) and its derivative p′(x) split in D[x]. We give a complete description of all D-nice symmetric polynomials with four roots over integral domains D of any characteristic not equal to 2 by giving an explicit formula for constructing these polynomials and by counting equivalence classes of such D-nice po...
متن کاملA DESCRIPTION OF n-ARY SEMIGROUPS POLYNOMIAL-DERIVED FROM INTEGRAL DOMAINS
We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing G lazek and Gleichgewicht’s classification of ternary semigroups.
متن کاملThe Diophantine Problem for Polynomial Rings and Fields of Rational Functions1
We prove that the diophantine problem for a ring of polynomials over an integral domain of characteristic zero or for a field of rational functions over a formally real field is unsolvable.
متن کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
متن کامل