On the relationship between the length of an algebra and the index of nilpotency of its Jacobson radical.

DOI10.1134/S0001434613110047zbMath1288.16025OpenAlexW2073984155MaRDI QIDQ2439975

O. V. Markova

Publication date: 26 March 2014

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434613110047

zbMATH Keywords

Jacobson radicalidealssubalgebrasalgebras over fieldslengths of algebrasquotient algebrasindices of nilpotency

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Finite rings and finite-dimensional associative algebras (16P10) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Jacobson radical, quasimultiplication (16N20)

Related Items (5)

On the lengths of group algebras of finite abelian groups in the semi-simple case ⋮ An example of length computation for a group algebra of a noncyclic abelian group in the modular case ⋮ Systems of generators of matrix incidence algebras over finite fields ⋮ Length of the group algebra of the dihedral group of order \(2^k\) ⋮ On the lengths of group algebras of finite abelian groups in the modular case

Cites Work

• Commutative matrix subalgebras and length function
• An upper bound for the length of a finite-dimensional algebra
• Lengths of finite dimensional representations of PBW algebras
• On some properties of the length function.
• Length computation of matrix subalgebras of special type.
• Upper bound for the length of commutative algebras
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