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On N-algebraic power series having polynomial growths
Tekijät: Honkala J
Kustantaja: MARCEL DEKKER INC
Julkaisuvuosi: 2000
Journal: Communications in Algebra
Tietokannassa oleva lehden nimi: COMMUNICATIONS IN ALGEBRA
Lehden akronyymi: COMMUN ALGEBRA
Vuosikerta: 28
Numero: 7
Aloitussivu: 3253
Lopetussivu: 3264
Sivujen määrä: 12
ISSN: 0092-7872
DOI: https://doi.org/10.1080/00927870008827022
Tiivistelmä
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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