Table of contents

Let be a semisimple -ring and its center. Assume that for any prime ideal the ring is primary. Let be the intersection of the maximal over-rings of , and . We prove that has a finite number of indecomposable integral representations if and only if is a hereditary ring, has two generators as a -module, and is cyclic.

In this paper we prove that the group of universal norms of a formal group corresponding to an elliptic curve of one of the three main types defined over a quasilocal field [11] is trivial. Applications are also indicated. Bibliography: 12 items.

In this paper we describe the quiver representations (see Manuscripta Math. 6(1972), 71-103) which do not contain the problem of reducing a pair of matrices by similarity transformations.

We classify up to G-isomorphism all normal affine irreducible quasihomogeneous (i.e. containing a dense orbit) varieties of the group G = SL(2) which are defined over an algebraically closed field of characteristic zero.

In this paper we describe algebraic K3 surfaces on which lie hyperelliptic curves. We prove a direct and an inverse theorem on the representation of such surfaces as a double plane. We explain the connection between surfaces of this type and elliptic surfaces.

For the existence of a nonsingular contraction (dilatation) of an analytic set on an n-dimensional complex manifold it is proved to be necessary and sufficient that there exist a formal nonsingular contraction (dilatation) of the analytic set.

In this paper one studies the local topological structure of analytic mappings. It is proved that the complement in the space of all germs of analytic mappings from Cⁿ to C^q of the set of germs whose topological type is unchanged under alteration of large terms of the Taylor series has infinite codimension.

The main theorem states that if the Spivak normal fibration associated to a Poincaré complex admits a vector bundle structure, then the Poincaré complex is homotopy equivalent to the union of two smooth manifolds with their boundaries identified via a homotopy equivalence. The theorem is applied to the question of existence of smooth structures on Poincaré complexes.

Let G be a region in the complex plane; let H be the space of functions analytic in G with the topology of uniform convergence on compacta of G; let W be a nontrivial invariant (with respect to differentiation) subspace in H which admits a spectral synthesis. We investigate conditions for which all functions of W can be analytically continued to a larger region .

In this article we prove that the Riesz equality holds for conjugate functions which are Denjoy integrable in the restricted sense. As a corollary one obtains that if the conjugate function is Denjoy integrable in the restricted sense, then the conjugate series coincides with the Fourier-Denjoy series of the conjugate function.