Let H be a Krull monoid with finite class group such that each class contains a prime divisor (e.g., the multiplicative monoid of the ring of algebraic integers of some number field). It is shown that it can be determined whether the class group is of the form Z/nZ ⊕ Z/nZ, for n ≥ 3, just by considering the system of sets of lengths of H.

The general Galois theory for functions and relational constraints over arbitrary sets described in the authors’ previous paper is refined by imposing algebraic conditions on relations.

Let X be a smooth algebraic curve. Suppose that there exists a triple covering f : X → Y where Y is a smooth algebraic curve. In this paper, we investigate the existence of morphisms from X to the projective line P which do not factor through the covering f . For this purpose, we generalize the classical results of Maroni concerning base-point-free pencils on trigonal curves to the case of trip...

If α1, . . . , αr are algebraic numbers such that N = r ∑

A brief survey of real algebraic structures on topological spaces is given.

This is the first paper in a series of three where we develope a systematic approach to the geometric algebras of multivectors and ex-tensors. The series is followed by another one where those algebraic concepts are used in a novel presentation of the differential geometry of (smooth) manifolds of arbitrary global topology. The key calcu-lational tool in our program is the euclidean geometrical...

Inspired by p-adic (and real) principal value integrals, we introduce motivic principal value integrals associated to multi-valued rational differential forms on smooth algebraic varieties. We investigate the natural question whether (for complete varieties) this notion is a birational invariant. The answer seems to be related to the dichotomy of the Minimal Model Program.

We present a set of planar parallel manipulators of Stewart Gough type which are singular with respect to the Schönflies group X(a) without being architecturally singular. This set of so called Schönflies-singular planar parallel manipulators is characterized by the property that the carrier plane of the platform or of the base anchor points is orthogonal to the rotational axis a of the Schönfl...

We study excursions with jumps to nearest neighbors in different lattices (hexagonal, triangular, kagome, Manhattan lattices), paths in a strip, etc. We show that some families are algebraic, D-finite, and give some nice closed form formulas.

We establish an algebraic version of the classical result that a G-map f between G-complexes which restricts to a homotopy equivalence fH on H-fixed sets for all subgroups H of G is a G-homotopy equivalence. This is used to give an alternative proof of a theorem of Bouc. We also include a number of illustrations and applications.