An introduction to multialgebras

Abstract

This thesis reviews the notion of a multialgebra. It gathers together the main ideas from a number of papers which have been written in a seemingly haphazard fashion over several years by various people and expounds them in a systematic way while also seeking to develop further results from them. Fundamental properties of homomorphisms (including weak homomorphisms), congruence relations and submultialgebras are obtained and the usual algebraic concepts of direct products, subdirect products, direct and inverse limits and polynomials are defined for multialgebras. Some general properties associated with these are derived and connections between multialgebras and universal algebras and multialgebras and topological spaces are investigated.