Quasi-multipliers on topological semigroups and their Stone–Čech 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 (S). First, we study the problem of extension of quasi-multipliers on topological semigroups to its Stone–Čech compactification. Indeed, we prove if S is a topological semigroup such that S × S is pseudocompact, then (S) can be regarded as a subset of (β S). Moreover, with an extra condition we describe (S) as a quotient subsemigroup of β S. Finally, we investigate quasi-multipliers on topological semigroups, its relationship with multipliers and give some concrete examples. [ABSTRACT FROM AUTHOR]