Left Regular and Right Regular Elements of Semigroups of 1-1 Transformations and 1-1 Linear Transformations
Yupaporn Kemprasit · 2010
An element x of a semigroup S is said to be left [right] regular if x = yx 2 [x = x 2 y] for some y ∈ S, or equivalently, xLx 2 [xRx 2 ]. In this paper, we characterize the left regular and right regular elements of the semigroups under composition of all 1-1 transformations of a set and of all 1-1 linear transformations of a vector space. Mathematics Subject Classification: 20M17, 20M20