be the set of (iso-classes of) finite dimensional simple right A-modules. An ndimensional simple A-module V ∈ Simpn(A) defines a surjectiv homomorphism of k-algebras, ρ : A → Endk(V ), the kernel of which is a two-sided maximal ideal mV , of A. Let Max≤∞ be the set of all such maximal ideals of A, for n ≥ 1. To exclude some strange and for our purposes non-interesting cases, we shall assume tha...

Two countable lters on ! are incompatible if they have no common innnite pseudo-intersection. Letting a(P f) denote the minimal size of a maximal uncountable family of pairwise incompatible countable lters on !, we prove the consistency of t < a(P f).

The aim of this work is to prove the nonexistence of complex structures over nilpotent Lie algebras of maximal class (also called filiform).

Let K be a global field or Q, F a nonzero quadratic form on KN , N ≥ 2, and V a subspace of KN . We prove the existence of an infinite collection of finite families of small-height maximal totally isotropic subspaces of (V, F ) such that each such family spans V as a K-vector space. This result generalizes and extends a well known theorem of J. Vaaler [16] and further contributes to the effecti...

It is well known in the work of Kadison and Ringrose 1983 that if A and B are maximal abelian von Neumann subalgebras of von Neumann algebras M and N, respectively, then A⊗B is a maximal abelian von Neumann subalgebra of M⊗N. It is then natural to ask whether a similar result holds in the context of JW-algebras and the JW-tensor product. Guided to some extent by the close relationship between a...

We show that soluble groups G of type Bredon-FP∞ with respect to the family of all virtually cyclic subgroups of G are always virtually cyclic. In such a group centralizers of elements are of type FP∞. We show that this implies the group is polycyclic. Another important ingredient of the proof is that a polycyclic-by-finite group with finitely many conjugacy classes of maximal virtually cyclic ...

In the present paper I show that one can recover much of the inertia structure of Zariski (quasi) divisors of a function field K|k over an algebraically closed base field k from the maximal pro-` abelian-by-central Galois theory of K. The results play a central role in the birational anabelian geometry and related questions.

For a countably generated group K and a function on K taking values that are either nonnega-tive integers or 1, we determine in Theorem 8 equivalent conditions for there to exist a Dedekind domain D with class group K such that, for each k in K, exactly (k) maximal ideals of D belong to k.

In the paper, we extend the definition of generalized derivations to superalgebras and prove that a generalized superderivation g on a prime superalgebra A is represented as g(x) = ax + d(x) for all x ∈ A, where a is an element of Qmr (the maximal right ring of quotients of A) and d is a superderivation on A. Using the result we study two generalized superderivations when their product is also ...

Let T be a triangle with two specified vertices v0, v1 ∈ Z2. A convex lattice chain in T from v0 to v1 is defined naturally (see the next paragraph). In this paper we prove what the maximal length of a convex lattice chain is if the area of T is fixed (and large). It is also shown that the solution is unique apart from lattice preserving affine transformations.