DERIVATIONS OF FINITARY INCIDENCE RINGS

Let l be a pocategory, (see Khripchenko [3]), and FI(l) its finitary incidence ring [3]. We prove that the ring ODer FI of outer derivations of FI(l) is isomorphic to the ring ODer l of outer derivations of l. Furthermore, if l = l(P, R), where P is a quasiordered set and R is a ring, then it is proved that ODer FI congruent to H-1 ((P) over bar, C(R)) x Pi(i is an element of I) ODerR. As a consequence, the description of the algebra K- ODer FI of outer K- derivations of FI(P,A), where A is a K- algebra, is obtained. The ring of outer derivations and the algebra of outer K- derivations of the weak incidence ring I*(l) [3] are also described.