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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On ideals of free and free nilpotent Lie algebras
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by Melih Boral PDF
Proc. Amer. Math. Soc. 94 (1985), 23-28 Request permission

Abstract:

It is proved that in a free nilpotent Lie algebra there are no nonabelian ideals which are free nilpotent as subalgebras. It is also shown that, for any proper ideal $S$ of a free Lie algebra $F$, the quotient of the lower central terms ${F_m}/{S_m}$ is not finitely generated when $F \ne {F_2} + S$. If $F = {F_2} + S,\;F/S$ is finite-dimensional and $S$ is finitely generated as an ideal in $F$, then ${F_m}/{S_m}$ is finitely generated as an algebra for all $m \geqslant 1$.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 23-28
  • MSC: Primary 17B65
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0781048-6
  • MathSciNet review: 781048