Geodesic
A Maximality Criterion for Nilpotent Commutative Matrix Algebras
Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 125-126

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be a commutative algebra contained in Mn (F), F a field. Then A is nilpotent if there exists v such that A v =(0), and is said to have nilpotency class k (denoted Cl(A)=k) if A k =(0), but A k-1≠(0). A well known result asserts that matrix algebras are nilpotent if and only if every element is nilpotent. Let N = {A | A is a nilpotent commutative subalgebra of M n (F)}. 
Handelman, D.; Selick, P. A Maximality Criterion for Nilpotent Commutative Matrix Algebras. Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 125-126. doi: 10.4153/CMB-1974-024-5
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[1] 1. Suprenenko, D. A., and Tyshkevich, R. I., Commutative matrices, Academic Press, New York, 1968. Google Scholar

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