On a conjecture of V. V. Shchigolev

Details On a conjecture of V. V. Shchigolev On a conjecture of V. V. Shchigolev

2009-11-09

arxiv.org/abs/0911.1709v2

Journal of Algebra 330 (2011), 314-321

Mathematics

Rings and Algebras

Scientific paper

10.1016/jalgebra.2010.12.015

V. V. Shchigolev has proven that over any infinite field k of characteristic p>2, the T-space generated by G={x_1^p,x_1^px_2^p,...} is finitely based, which answered a question raised by A. V. Grishin. Shchigolev went on to conjecture that every infinite subset of G generated a finitely based T-space. In this paper, we prove that Shchigolev's conjecture was correct by showing that for any field of characteristic p>2, the T-space generated by any subset {x_1^px_2^p...x_{i_1}^p, x_1^px_2^p...x_{i_2}^p,...}, i_1

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