Lattice structure tl-ideals of tl-subsemigroups

In mathematics, many methods have been used to determine special semigroups, groups, rings and modules. One of these is to examine the lattice structures of subalgebraic structures. In particular, the lattice structures of subgroups of a group and whether a group is a cyclic group, abelian group and p-group have been determined. After this view, TL- subalgebraic structures (in particular T=T_M or L=[0,1]) have been examined in terms of lattice, complete lattice, modular lattice and distributed lattice. The subject of this thesis is to investigate the properties of the lattice structures by examining the TL-left(right) ideals, bi-ideals, quasi ideals, interior ideals and their relations of a TL- subsemigroup in semigroups. With the help of the properties of the lattice structures, the characterization of special semigroups will be discussed. In addition, the image reverse view of these structures will be examined under semigroup homomorphism. Further, the effect of such structures on the cartesian product of semigroups will be investigated. Based on previous studies, it will be synthesized and new theorems will be given.