By substantial changes and corrections in Demushkinâ€™s old paper the essentially final positive answer to the isomorphism problem for monoid rings of submonoids of Zâ€™ is obtained. This means that theâ€¦ (More)

We investigate the minimal number of generators Î¼ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalitiesâ€¦ (More)

Preface For every mathematician, ring theory and K-theory are intimately connected: algebraic K-theory is largely the K-theory of rings. At first sight, polytopes, by their very nature, must appearâ€¦ (More)

For n â‰¥ 6 we provide a counterexample to the conjecture that every integral vector of a n-dimensional integral polyhedral pointed cone C can be written as a nonnegative integral combination of atâ€¦ (More)

We investigate similarities between the category of vector spaces and that of polytopal algebras, containing the former as a full subcategory. In Section 2 we introduce the notion of a polytopalâ€¦ (More)

SÌ„ = {x âˆˆ gp(S) | mx âˆˆ S for some m > 0}. One calls S normal if S = SÌ„. For simplicity we will often assume that gp(S) = Z; this is harmless because we can replace Z by gp(S) if necessary. The rankâ€¦ (More)

It is shown that all nontrivial elements in higher K-groups of toric varieties are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality ofâ€¦ (More)

Let P be ad-dimensional lattice polytope. We show that there exists a natural numbercd, only depending ond, such that the multiples cP have a unimodular cover for everycâˆˆ N, câ‰¥ cd. Actually, aâ€¦ (More)

In this note we show that the nilpotence conjecture for toric varieties is true over any regular coefficient ring containing Q. In [G] we showed that for any additive submonoid M of a rational vectorâ€¦ (More)