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 -