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Irreducibility of an affine space in algebraic geometry over a group

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Algebra and Logic Aims and scope

We prove a theorem which states that if G is an equationally Noetherian group that is locally approximated by finite p-groups for each prime p then an affine space G n in a respective Zariski topology is irreducible for any n. The hypothesis of the theorem is satisfied by free groups, free soluble groups, free nilpotent groups, finitely generated torsion-free nilpotent groups, and rigid soluble groups. Also corrections to a valuation lemma, which has been used in some of the author’s previous works, are introduced.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    N. S. Romanovskii

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    N. S. Romanovskii

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  1. N. S. Romanovskii
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Correspondence to N. S. Romanovskii.

Additional information

Translated from Algebra i Logika, Vol. 52, No. 3, pp. 386-391, May-June, 2013.

*Supported by RFBR, project No. 12-01-00084.

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Romanovskii, N.S. Irreducibility of an affine space in algebraic geometry over a group. Algebra Logic 52, 262–265 (2013). https://doi.org/10.1007/s10469-013-9239-4

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  • DOI: https://doi.org/10.1007/s10469-013-9239-4

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