On Ranges of Polynomials in Finite Matrix Rings

DOI10.2307/2048069zbMath0714.16015OpenAlexW4242309622MaRDI QIDQ3199597

Chen-Lian Chuang

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2048069

zbMATH Keywords

identitiesmatrix algebrafinite fieldrangecentral polynomialsfree associative algebra

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Finite rings and finite-dimensional associative algebras (16P10) Finite fields (field-theoretic aspects) (12E20) Semiprime p.i. rings, rings embeddable in matrices over commutative rings (16R20)

Related Items (13)

The images of multilinear polynomials evaluated on $3\times 3$ matrices ⋮ Word equations in simple groups and polynomial equations in simple algebras. ⋮ Values of polynomials on centrally closed prime algebras ⋮ Images of multilinear graded polynomials on upper triangular matrix algebras ⋮ The images of multilinear and semihomogeneous polynomials on the algebra of octonions ⋮ The Waring problem for matrix algebras ⋮ Evaluations of noncommutative polynomials on algebras: methods and problems, and the L'vov-Kaplansky conjecture ⋮ Polynomials which permute matrices over commutative antinegative semirings ⋮ The images of noncommutative polynomials evaluated on the quaternion algebra ⋮ Commutators and images of noncommutative polynomials ⋮ Right ideals generated by an idempotent of finite rank. ⋮ On Fagundes-Mello conjecture ⋮ The images of non-commutative polynomials evaluated on 2×2 matrices

Cites Work

• Unnamed Item
• The additive subgroup generated by a polynomial
• Periodic and Nil Polynomials in Rings
• Nil and Power-Central Polynomials in Rings
• A Characterization of the n × n Matrices Over a Finite Field
• "Problems in the Theory of Rings" Revisited

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