STRUCTURE OF INCIDENCE ALGEBRAS OF LOCALLY FINITE PARTIALLY ORDERED SET - EFIYANTI (NIM 20106013), GUSTINA
Let E be an equivalence relation on the set of non empty interval of P. A function f I(P,F) is an E-function if f is constant on equivalence classes of E. Let I(PE,F) be the collection of E-function, we call an equivalence relation E order compatible if the E-function closed under multiplication in I(P,F). This thesis considers necessary and sufficient condition of I(PE,F) to be a sub algebra of I(P,F). It also give an application of incidence algebras in physics, that is if the partially ordered set was simplicial complexes K then its incidence algebra has the structure of differential module over algebra of all complex-valued function on K. It would be a basis for discrete approximation of spacetime structure.