Semigroup Arrising From Trellises

Abstract This study explores semigroups, which are algebraic structures with an associative binary operation, that arise from trellis structures. The research investigates the formation and properties of these semigroups. It is proven that the set of all functions from a trellis L to itself, denoted T(L), also forms a trellis. The concept of an order-preserving map in T(L) is discussed. The study demonstrates that the sets of all join homomorphisms on L (J(L)), all meet homomorphisms on L (M(L)), and all endomorphisms on L (E(L)) are submonoids of T(L). Additionally, it is observed that the set of all Automorphisms of L (Aut(L)) forms a group with respect to function composition. The study further discusses the conditions under which monoids like T(L), J(L), M(L), E(L), and Aut(L) are isomorphic to their corresponding monoids arising from another trellis L'. 2020 Mathematical Sciences Classification: 06D75.