Some Results of Ideals for Partial Transformation Semigroups - Al-Aadhami, Asawer; Aubad, Ali Abd (Iraqi Journal of Science, 2026)
Let 〖PT〗_n be the set of all partial functions from the set N to the set M, where N, M⊆X_n and X_n=1,2,…,n. Then 〖PT〗_n is a semigroup subject to the composition of partial mapping or a monoid with identity PI_n. Here, the ideal of 〖PT〗_n in terms of an element ξ∈ T ̃_(n,0) was studied, where T ̃_(n,0) is full transformation monoid from the set X_(n,0) to itself such that X_(n,0)=0∪X_n. Finding that there are two kinds of ideals in 〖PT〗_n, two-sided ideals, and a left ideal. As well as the ideals of partial transformation monoid of a free (left) G -act on n-generators, 〖PT〗_(F_n (G)) where G is a finite group and F_n (G)=∪ ̇_(i=1)^n Gx_i were considered. Finally, the number of elements of a two-sided ideal and left ideal of 〖PT〗_n and 〖PT〗_(F_n (G)) were also found.