The effect of assuming the identity as a generator on the length of the matrix algebra

DOI10.1016/j.laa.2015.09.021zbMath1334.15051arXiv1501.05806OpenAlexW2963303736MaRDI QIDQ269289

Helena Šmigoc, Thomas J. Laffey, O. V. Markova

Publication date: 18 April 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.05806

zbMATH Keywords

finitely generated algebralengths of algebras

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Algebraic systems of matrices (15A30) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

Related Items (6)

On the lengths of standard composition algebras ⋮ Values of the length function for nonassociative algebras ⋮ A resolution of Paz's conjecture in the presence of a nonderogatory matrix ⋮ Systems of generators of matrix incidence algebras over finite fields ⋮ -MINIMUM SPANNING LENGTHS AND AN EXTENSION TO BURNSIDE’S THEOREM ON IRREDUCIBILITY ⋮ Algebras of slowly growing length

Cites Work

• Commutative matrix subalgebras and length function
• Pairs of matrices with quadratic minimal polynomials
• Algebras generated by two idempotents
• An upper bound for the length of a finite-dimensional algebra
• Lengths of finite dimensional representations of PBW algebras
• Burnside's theorem: Irreducible pairs of transformations
• The algebra of semimagic matrices and its length
• Length computation of matrix subalgebras of special type.
• The length function and matrix algebras
• On the lengths of irreducible pairs of complex matrices
• ON THE LENGTHS OF PAIRS OF COMPLEX MATRICES OF SIZE SIX
• An application of the Cayley-Hamilton theorem to matrix polynomials in several variables
• On the lengths of pairs of complex matrices of size at most five
• A Pair of Matrices with Property P

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