Quasi-multipliers on topological semigroups and their Stone-Cech compactification

In this paper, we introduce and study the notion of quasi-multipliers on a semi-topological semigroup S. The set of all quasi-multipliers on S is denoted by QM(S). First, we study the problem of extension of quasi-multipliers on topological semigroups to its Stone-Cech compactification. Indeed, we prove if S is a topological semigroup such that S x S is pseudocompact, then QM(S) can be regarded as a subset of QM(beta S). Moreover, with an extra condition we describe QM(S) as a quotient subsemigroup of beta S. Finally, we investigate quasi-multipliers on topological semigroups, its relationship with multipliers and give some concrete examples.