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An algebra which is a maximal commutative subalgebra in very few algebras

Volume 147 / 2017

Wiesław Żelazko Colloquium Mathematicum 147 (2017), 241-246 MSC: Primary 16S50; Secondary 46H10; 47L10. DOI: 10.4064/cm6941-6-2016 Published online: 13 January 2017

Abstract

“Very few” in the title means two. We show that a unital real or complex algebra generated by a nilpotent of order two can be a maximal abelian subalgebra only in two algebras. One of them is of dimension three and the other of dimension four.

Authors

  • Wiesław ŻelazkoInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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