TY - JOUR
T1 - About Height Theorem
AU - Belov, A. J.
PY - 1995/1
Y1 - 1995/1
N2 - Let A be a PI-algebra with generators {ai}, i = 1, …, k and Wnbe a set of all words in {ai} with length less or equal n, where n is PI-degree of A. If all elements of Wnare algebraic, then A is finite dimensional. This theorem was firstly proved by V. Ufnarovsky, but the proof was too difficult. In this paper we give the short one. It based on the upper boundary for the height of algebra A, and on the consideration of infinite words (superwords) in algebras.
AB - Let A be a PI-algebra with generators {ai}, i = 1, …, k and Wnbe a set of all words in {ai} with length less or equal n, where n is PI-degree of A. If all elements of Wnare algebraic, then A is finite dimensional. This theorem was firstly proved by V. Ufnarovsky, but the proof was too difficult. In this paper we give the short one. It based on the upper boundary for the height of algebra A, and on the consideration of infinite words (superwords) in algebras.
UR - http://www.scopus.com/inward/record.url?scp=58249123958&partnerID=8YFLogxK
U2 - 10.1080/00927879508825416
DO - 10.1080/00927879508825416
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AN - SCOPUS:58249123958
SN - 0092-7872
VL - 23
SP - 3551
EP - 3553
JO - Communications in Algebra
JF - Communications in Algebra
IS - 9
ER -