Linear relations between roots of polynomials
Kurt Girstmair (1999)
Acta Arithmetica
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Kurt Girstmair (1999)
Acta Arithmetica
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Alan G. B. Lauder (1999)
Acta Arithmetica
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D. R. Heath-Brown (1997)
Acta Arithmetica
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Christopher McCord (1997)
Fundamenta Mathematicae
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Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), is introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number....
Rüdiger Göbel, Simone Pabst (1998)
Fundamenta Mathematicae
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The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain