Displaying similar documents to “The irreducible components of the nilpotent associative algebras.”

Group Gradings on Free Algebras of Nilpotent Varieties of Algebras

Bahturin, Yuri (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 16W50, 17B70; Secondary 16R10. The main result is the classification, up to isomorphism, of all gradings by arbitrary abelian groups on the finitely generated algebras that are free in a nilpotent variety of algebras over an algebraically closed field of characteristic zero. The research was supported by an NSERC Discovery Grant #227060-09

Homomorphic images of finite subdirectly irreducible unary algebras

Jaroslav Ježek, P. Marković, David Stanovský (2007)

Czechoslovak Mathematical Journal

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We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty.

Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras.

Sergio A. Albeverio, Ayupov, Shavkat, A. 2, Bakhrom A. Omirov (2006)

Revista Matemática Complutense

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In this work the properties of Cartan subalgebras and weight spaces of finite dimensional Lie algebras are extended to the case of Leibniz algebras. Namely, the relation between Cartan subalgebras and regular elements are described, also an analogue of Cartan s criterion of solvability is proved.