Homomorphic images of pro-nilpotent algebras

@inproceedings{Bergman2009HomomorphicIO,
  title={Homomorphic images of pro-nilpotent algebras},
  author={George M. Bergman},
  year={2009}
}
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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SHOWING 1-10 OF 24 REFERENCES

An example of a simple radical ring

  • E. Sa̧siada, P. M. Cohn
  • J. Algebra
  • 1967
Highly Influential
6 Excerpts

Linear maps on kI

  • G. M. Bergman, N. Nahlus
  • and homomorphic images of infinite direct product…
  • 2012
2 Excerpts

The Lie theory of connected pro-Lie groups

  • K. H. Hofmann, S. A. Morris
  • A structure theory for pro-Lie algebras, pro-Lie…
  • 2007
1 Excerpt

Algebra

  • S. Lang
  • 3rd ed., Addison-Wesley, Reading, ; reprinted as…
  • 2002

Lectures on modules and rings

  • T. Y. Lam
  • Graduate Texts in Mathematics, vol. 189, Springer…
  • 1999

M

  • J. D. Dixon
  • P. F. du Sautoy, A. Mann and D. Segal, Analytic…
  • 1999

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