Central polynomials in the matrix algebra of order two. (Q1418967)

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.