Homomorphic images of pro-nilpotent algebras

  title={Homomorphic images of pro-nilpotent algebras},
  author={George M. Bergman},
It is shown that any finite-dimensional homomorphic image of an inverse limit of nilpotent not-necessarily-associative algebras over a field is nilpotent. More generally, this is true of algebras over a general commutative ring k, with “finitedimensional” replaced by “of finite length as a k-module.” These results are obtained by considering the multiplication algebra M(A) of an algebra A (the associative algebra of k-linear maps A → A generated by left and right multiplications by elements of… CONTINUE READING

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