2000•Unpublished venueOpen access

Exponents of Subvarieties of Upper Triangular Matrices over Arbitrary Fields are Integral

Victor Petrogradsky

Abstract

Abstract. Let Uc be the variety of associative algebras generated by the algebra of all upper triangular matrices, the field being arbitrary. We prove that the upper exponent of any subvariety V ⊂ Uc coincides with the lower exponent and is an integer. 1. Codimension growth and exponents. Let K denote the ground field, we consider it to be arbitrary. Suppose that V is a variety of (associative) algebras, this is the class of all algebras that satisfy some fixed set of identical relations. Let F (V,X) be its free algebra generated by a countable set of gen-erators X = {xi | i ∈ N}. We denoteby Pn(V) ⊂ F (V,X) the subspace of all

About this research paper

What this paper is about

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Subvariety, Mathematics, Triangular matrix, Exponent, Integer (computer science), Variety (cybernetics), Associative property, Field (mathematics)