Central polynomials in the matrix algebra of order two. (English) Zbl 1044.16016
The authors exhibit a minimal basis of the polynomial identities for \(M_2(K)\), the algebra of \(2\times 2\) matrices over an infinite field \(K\), whose characteristic \(p\) is positive and is different from \(2\). When \(p>3\), the standard identity of degree \(4\) and the Hall identity generate the T-ideal of \(M_2(K)\), just like in characteristic zero; when \(p=3\), one needs an additional identity. Furthermore, using this result, a minimal set of generators of the T-space of central polynomials for \(M_2(K)\) is given.
Reviewer: Matyas Domokos (Budapest)
MSC:
| 16R10 | \(T\)-ideals, identities, varieties of associative rings and algebras |
| 16R20 | Semiprime p.i. rings, rings embeddable in matrices over commutative rings |
| 16S50 | Endomorphism rings; matrix rings |
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