A1 Refereed original research article in a scientific journal
On N-algebraic power series having polynomial growths
Authors: Honkala J
Publisher: MARCEL DEKKER INC
Publication year: 2000
Journal: Communications in Algebra
Journal name in source: COMMUNICATIONS IN ALGEBRA
Journal acronym: COMMUN ALGEBRA
Volume: 28
Issue: 7
First page : 3253
Last page: 3264
Number of pages: 12
ISSN: 0092-7872
DOI: https://doi.org/10.1080/00927870008827022
Abstract
We study polynomial growth of algebraic series. It is proved that if an N-algebraic series tau with arbitrarily many commuting variables has polynomial growth, then tau is in fact N-rational. Also, polynomial growth is decidable. Similar results are proved for N-algebraic series with noncommuting variables having bounded supports. It is also shown that polynomial growth is not decidable for N-algebraic series having noncommuting variables without the additional condition on the supports.
We study polynomial growth of algebraic series. It is proved that if an N-algebraic series tau with arbitrarily many commuting variables has polynomial growth, then tau is in fact N-rational. Also, polynomial growth is decidable. Similar results are proved for N-algebraic series with noncommuting variables having bounded supports. It is also shown that polynomial growth is not decidable for N-algebraic series having noncommuting variables without the additional condition on the supports.
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