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A Maximality Criterion for Nilpotent Commutative Matrix Algebras

Published online by Cambridge University Press:  20 November 2018

D. Handelman  and
P. Selick
D. Handelman
Affiliation:
McGill University, Montreal, Quebec
P. Selick
Affiliation:
University of Toronto, Toronto, Ontario
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Let A be a commutative algebra contained in Mn(F), F a field. Then A is nilpotent if there exists v such that Av=(0), and is said to have nilpotency class k (denoted Cl(A)=k) if Ak=(0), but Ak-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 Mn(F)}.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 125 - 126
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Suprenenko, D. A., and Tyshkevich, R. I., Commutative matrices, Academic Press, New York, 1968.Google Scholar