IJPAM: Volume 71, No. 3 (2011)

TEST RANK OF THE LIE ALGEBRA $F/R^{^{\prime }}$

Nazar Şahin Öğüşlü
Department of Mathematics
Çukurova University
Adana, TURKEY


Abstract. Let $F$ be a free Lie algebra of rank $n\geq 2$ and $R=F^{n_{1},n_{2},...,n_{k}}$. We prove that the test rank of the Lie algebra $F/R^{^{\prime }}$ is $n-1$.

Received: June 6, 2009

AMS Subject Classification: 17B01, 17B40

Key Words and Phrases: automorphism, free Lie algebras, test elements, test sets, test rank

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 3