### Equivalence of the strengthened Hanna Neumann conjecture and the amalgamated graph conjecture.

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Attention is drawn to an error in W. S. Jassim's paper.

A direct proof of Braun's characterization of Azumaya algebras is given.

We use hyperbolic geometry to study the limiting behavior of the average number of ways of expressing a number as the sum of two coprime squares. An alternative viewpoint using analytic number theory is also given.

Pere Menal, Professor of Algebra at the Universitat Autònoma de Barcelona, died in a traffic accident on April 4th, 1991. His colleagues in the Mathematics Department of the UAB strongly felt the need to pay a tribute to his memory, and decided then to dedicate this, the Autumn 1992 issue of the departmental journal, to his memory.

We conjecture that every finite group G acting on a contractible CW-complex X of dimension 2 has at least one fixed point. We prove this in the case where G is solvable, and under this additional hypothesis, the result holds for X acyclic.

To a commutative ring K, and a family of K-algebras indexed by the vertex set of a graph, we associate a K-algebra obtained by a mixture of coproduct and tensor product constructions. For this, and related constructions, we give exact sequences and deduce homological properties.

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