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arXiv · 1403.4201

Graded polynomial identities and central polynomials of matrices over an infinite integral domain

Luís Felipe Gonçalves Fonseca
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Abstract

Let $K$ be an infinite integral domain and $M_{n}(K)$ be the algebra of all $n\times n$ matrices over $K$. This paper aims for the following goals: Find a basis for the graded identities for elementary grading in $M_{n}(K)$ when the neutral component and diagonal coincide; Describe the $\mathbb{Z}_{p}$-graded central polynomials of $M_{p}(K)$ when $p$ is a prime number; Describe the $\mathbb{Z}$-graded central polynomials of $M_{n}(K)$.

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Luís Felipe Gonçalves Fonseca. 2014-03-17. Graded polynomial identities and central polynomials of matrices over an infinite integral domain. https://doi.org/10.1007/s12215-014-0174-6

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