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arXiv · 1711.09435

Almost nilpotency of an associative algebra with an almost nilpotent fixed-point subalgebra

Makarenko Natalia
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Abstract

Let A be an associative algebra of arbitrary dimension over a field F and G a finite soluble group of automorphisms of A oforder n, prime to the characteristic of F. We prove that if the fixed-point subalgebra of A under the action of G contains a two-sided nilpotent ideal of nilpotency index d and of finite codimension m in I, then A contains a nilpotent two-sided ideal of nilpotency index bounded by a function of n and d and of finite codimension bounded by a function of m, n and d.

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Makarenko Natalia. 2017-11-26. Almost nilpotency of an associative algebra with an almost nilpotent fixed-point subalgebra. https://arxiv.org/abs/1711.09435

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