A note on varieties of unary algebras
Stanley Burris (1971)
Colloquium Mathematicae
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Stanley Burris (1971)
Colloquium Mathematicae
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Libor Polák (1977)
Archivum Mathematicum
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W. Bartol, D. Niwiński, L. Rudak (1985)
Colloquium Mathematicae
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Grishin, A.V. (2000)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Finogenova, Olga (2012)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 16R10, 16R40. We discuss characterizations of some non-matrix properties of varieties of associative algebras in the language of forbidden objects. Properties under consideration include the Engel property, Lie nilpotency, permutativity. We formulate a few open problems. * The author acknowledges support from the Russian Foundation for Basic Research, grant 10-01-00524.
Hilda Draškovičová, Jerzy Płonka (1991)
Mathematica Slovaca
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B. Wozniakowska (1985)
Semigroup forum
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Adam Hajduk (2006)
Colloquium Mathematicae
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The main aim of this note is to prove that if k is an algebraically closed field and a k-algebra A₀ is a CB-degeneration of a finite-dimensional k-algebra A₁, then there exists a factor algebra Ā₀ of A₀ of the same dimension as A₁ such that Ā₀ is a CB-degeneration of A₁. As a consequence, Ā₀ is a rigid degeneration of A₁, provided A₀ is basic.