(untitled) (European Journal of Pure and Applied Mathematics, 2022)
The variant of a semigroup S with respect to an element aS , is the semigroup with underlying set S and a new binary operation * defined by x* y=xay for x, yS . Let T(X) be the full transformation semigroup on a nonempty set X . For an arbitrary equivalence E on X , let \[T_E(X)={αT(X) : a, bX, (a, b)E (aα, bαE)}.\] Then T_E(X) is a subsemigroup of T(X) . In this paper, we investigate regular, left regular and right regular elements for the variant of some subsemigroups of the semigroup T_E(X) .