Many Valued Algebras

It is well known that contemporary mathematics includes many disci­ plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others.

Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings.

This volume presents papers from the Fourth Conference on Function Spaces. The conference brought together mathematicians interested in various problems within the general area of function spaces, allowing for discussion and exchange of ideas on those problems and related questions.

This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.

The area of mathematics surveyed by the present report might be described as a little too broad to be treated in an encyclopedic manner in a reasonable space and yet not sufficiently developed in all its parts to warrant several distinct reports. Group theory and lattice theory are both regarded as outside the scope of the report. Subject to this restriction, the area surveyed is the algebraic theory of systems with a single binary operation. The operation is understood to be single- valued except in the case of multigroups and allied systems. Since quasigroups, for example, can be studied either in terms of a single binary operation or in terms of three, a little of the theory of general algebras enters quite naturally. A diagram indicating the interrelations of the various systemswill be found at the end of Chapter li.