AUTOMORPHIC-DIFFERENTIAL IDENTITIES AND ACTIONS OF POINTED COALGEBRASON RINGS

In this paper, we prove the following two results which generalize the theorem concerning automorphic-differential endomorphisms asserted by J. Bergen. Let R be a ring, R-F its left Martindale quotient ring and U a right ideal of R having no nonzero left annihilator. (1) Let C be a pointed coalgebra which measures R such that the group-like element s of C act as automorphisms of R. If R is prime and xi.U = 0 for xi is an element of R#C, then xi.R = 0. Furthermore, if the action of C ext ends to R-F and if xi is an element of R-F#C such that xi.U = 0, then xi.R-F = 0. (2) Let f be an endomorphism of R-F given as a sum of comp osition maps of left multiplications, right multiplications, automorph isms and skew-derivations. If R is semiprime and f(U) = 0, then f(R) = 0.