(untitled) (European Journal of Pure and Applied Mathematics, 2018)
An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = Ma]. Let X be a nonempty set and T(X) be the semigroup of all transformation from X into itself under the composition of functions. For a partition P = X_Î±Â | Î± âˆˆ I of the set X, let T(X,P) = f âˆˆ T(X) | (X_Î±)f âŠ† X_Î±Â for all Î± âˆˆ I. Then T(X,P) is a subsemigroup of T(X) and if P = X,Â T(X,P) = T(X). Our aim in this paper is to give necessary and suï¬ƒcient conditions for elements in T(X,P) to be left or right magnifying. Moreover, we apply those conditions to give necessary and suï¬ƒcient conditions for elements in some generalized linear transformation semigroups.