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We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series r has a cyclic image if there is a rational number q such that all nonzero coefficients of r are integer powers of q.
@article{ITA_2011__45_4_375_0,
author = {Honkala, Juha},
title = {The cyclicity problem for the images of {Q-rational} series},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {375--381},
publisher = {EDP-Sciences},
volume = {45},
number = {4},
year = {2011},
doi = {10.1051/ita/2011111},
mrnumber = {2876112},
zbl = {1261.11027},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011111/}
}
TY - JOUR AU - Honkala, Juha TI - The cyclicity problem for the images of Q-rational series JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2011 SP - 375 EP - 381 VL - 45 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2011111/ DO - 10.1051/ita/2011111 LA - en ID - ITA_2011__45_4_375_0 ER -
%0 Journal Article %A Honkala, Juha %T The cyclicity problem for the images of Q-rational series %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2011 %P 375-381 %V 45 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2011111/ %R 10.1051/ita/2011111 %G en %F ITA_2011__45_4_375_0
Honkala, Juha. The cyclicity problem for the images of Q-rational series. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 4, pp. 375-381. doi: 10.1051/ita/2011111
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