The fundamental group of a triangular algebra without double bypasses

The Fundamental Theorem of Algebra: a Constructive Development without Choice

Is it reasonable to do constructive mathematics without the axiom of countable choice? Serious schools of constructive mathematics all assume it one way or another, but the arguments for it are not compelling. The fundamental theorem of algebra will serve as an example of where countable choice comes into play and how to proceed in its absence. Along the way, a notion of a complete metric space...

Group Invariant Integration and the Fundamental Theorem of Algebra.

The Fundamental Group of the Von Neumann Algebra of a Free Group with Infinitely

In this paper we show that the fundamental group !T of the von Neumann algebra 2(Foo) of a free (noncommutative) group with infinitely many generators is lR+ \ {O}. This extends the result of Voiculescu who previously proved [26,27] that Q+ \ {O} is contained in !T(2(Foo)). This solves a classical problem in the harmonic analysis of the free group F 00. In particular, it follows that there exis...

THE ANALOGUE OF WEIGHTED GROUP ALGEBRA FOR SEMITOPOLOGICAL SEMIGROUPS

In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the convolution measure algebra M, (S) of a locally compact semigroup. H. Dzinotyiweyi in [5,7] considers an analogous measure space on a large class of C-distinguished topological semigroups containing all completely regular topological semigroups. In this paper, we extend the definitions to study the weighted semigroup ...

Triangular Decomposition of the Composition Algebra of the Kronecker Algebra

Let A be a nite dimensional hereditary algebra over a nite eld, H(A) and C(A) be respectively the Ringel-Hall algebra and the composition algebra of A. Deene r d to be the element P M] 2 H(A), where M] runs over the isomorphism classes of the regular A?modules with dimension vector d. We prove that r d and the exceptional A?modules all lie in C(A). Let K be the Kronecker algebra, P (resp. I) th...