About Height Theorem

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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.

Original languageEnglish
Pages (from-to)3551-3553
Number of pages3
JournalCommunications in Algebra
Issue number9
StatePublished - Jan 1995
Externally publishedYes


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