TY - JOUR
TI - Left and Right Magnifying Elements in Generalized Semigroups of Transformations by Using Partitions of a Set
PY - 2018/07/31
Y2 - 2024/07/12
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 11
IS - 3
LA - en
DO - 10.29020/nybg.ejpam.v11i3.3260
UR - https://doi.org/10.29020/nybg.ejpam.v11i3.3260
SP - 580-588
AB - 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.
ER -