Abstract. 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 A 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 elements of C act as automorphisms of R. If R is prime and ξ · A = 0 for ξ ∈ R#C, then ξ · R = 0. Furthermore, if the action of C extends to R F and if ξ ∈ R F #C such that ξ · A = 0, then ξ · R F = 0. (2) Let f be an endomorphism of R F given as a sum of composition maps of left multiplications, right multiplications, automorphisms and skew-derivations. If R is semiprime and f (A) = 0, then f(R) = 0.
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