On N-algebraic power series having polynomial growths



: Honkala J

Publisher: MARCEL DEKKER INC

: 2000

: Communications in Algebra

: COMMUNICATIONS IN ALGEBRA

: COMMUN ALGEBRA

: 28

: 7

: 3253

: 3264

: 12

: 0092-7872

DOI: https://doi.org/10.1080/00927870008827022


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.



Last updated on 2024-26-11 at 14:47