Homogeneous varieties under split solvable algebraic groups

We present a modern proof of a theorem of Rosenlicht, asserting that every variety as in the title is isomorphic to a product of affine lines and punctured affine lines.     

Diophantine approximation by algebraic hypersurfaces and varieties

Questions on rational approximations to a real number can be generalized in two directions. On the one hand, we may ask about ``approximation' to a point in by hyperplanes defined over the rationals. That is, we seek hyperplanes with small distance from the given point. On the other hand, following Wirsing, we may ask about approximation to a real number by real algebraic numbers of degree at most .

The present paper deals with a common generalization of both directions, namely with approximation to a point in by algebraic hypersurfaces, or more generally algebraic varieties defined over the rationals.

     

Finiteness conditions in Jordan pairs

To Nathan Jacobson on his 80^th birthday     

On the varieties defined by Riemann-Mumford's relations

In this paper we consider varieties defined by Riemann-Mumford's relations. An irreducible component of these varieties is related to Siegel modular varieties. We prove that in most cases Riemann-Mumford varieties are not irreducible.

     

An algebraic proof that pseudovarieties are defined by pseudoidentities

An algebraic proof is given which shows that any pseudovariety of finite algebras is determined by a set of pseudoidentities.Presented by Boris M. Schein.     

Modular representations of simple Jordan pairs

Omsk. Translated fromSibirskii Matematicheskii Zhurnal, Vol. 32, No. 2, pp. 200–203, March–April, 1991.