Geodesic
Irreducibility of an affine space in algebraic geometry over a group
Algebra i logika, Tome 52 (2013) no. 3, pp. 386-391

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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 we introduce corrections to a lemma on valuations, which has been used in some of the author's previous works.
Keywords: Zariski topology, equationally Noetherian group, algebraic geometry over group.
Mots-clés : affine space 
@article{AL_2013_52_3_a6,
     author = {N. S. Romanovskii},
     title = {Irreducibility of an affine space in algebraic geometry over a~group},
     journal = {Algebra i logika},
     pages = {386--391},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_3_a6/}
}
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N. S. Romanovskii. Irreducibility of an affine space in algebraic geometry over a group. Algebra i logika, Tome 52 (2013) no. 3, pp. 386-391. http://geodesic.mathdoc.fr/item/AL_2013_52_3_a6/