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By L uroth's theorem, all intermediate elds of the extension |(x) : |, |an arbitrary eld, are simple. Those that contain a nonconstant polynomial, the polynomial rational function elds, constitute a sublattice (with respect to set inclusion). We give a fast algorithm for computing a generator of |(p; q), which is similar to the Euclidean algorithm, and also… (More)

- FRANZ BINDER
- 1995

Bidecompositions, i.e., solutions to r • p = s • q, play a central rôle in the study of uniqueness properties of complete decompositions with respect to functional composition. In [Rit22] all bidecompositions using polynomials over the complex number field have been characterized. Later the result was generalized to more general fields. All proofs tend to… (More)

In this note we present some algorithms to deal with nearrings, the appropriate algebraic structure to study non-linear functions. This is similar the role of rings in the theory of linear functions or that of groups for permutations. In particular, we give efficient algorithms that deal with big nearrings that are given by a small set of generators. In… (More)

In this note, we present algorithms to deal with finite near-rings, the appropriate algebraic structure to study non-linear functions on finite groups. Just as rings (of matrices) operate on vector spaces, near-rings operate on groups. In our approach, we have developed efficient algorithms for a variety of problems that involve the structure of the… (More)

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