Commutative Finite-Dimensional Algebras Satisfyingx(x(xy)) = 0 are Nilpotent

DOI10.1080/00927870802502944zbMath1205.17002OpenAlexW2147898859MaRDI QIDQ3646349

J. Carlos Gutiérrez Fernández

Publication date: 20 November 2009

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927870802502944

zbMATH Keywords

commutative algebranilpotentidentity

Mathematics Subject Classification ID

Power-associative rings (17A05) Nonassociative algebras satisfying other identities (17A30)

Related Items (8)

On commutative finite-dimensional nilalgebras ⋮ The space of invariant bilinear forms of the polarization algebra of a polynomial endomorphism: an approach to the problem of Albert ⋮ Power associative nilalgebras of dimension 9 ⋮ About nilalgebras satisfying (xy)² = x²y² ⋮ Linearly triangularizable quadratic endomorphisms ⋮ Polarization algebras and their relations ⋮ Nilpotency of commutative finitely generated algebras satisfying \(L_x^3+\gamma\, L_{x^3}\), \(\gamma =1,0\) ⋮ On Jordan-Nilalgebras of Index 3

Cites Work

• Commutative finitely generated algebras satisfying \(((yx)x)x=0\) are solvable
• Nilpotence of a class of commutative power-associative nilalgebras
• ON THE NILPOTENCE OF THE MULTIPLICATION OPERATOR IN COMMUTATIVE RIGHT NIL ALGEBRAS
• On Commutative Power-Associative Nilalgebras

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