Polinômios centrais para álgebras T-primas.

Abstract

In this work we study ordinary, Z2-graded central polinomials and central polinomials with involution for some important algebras in the theory of algebras with polinomial identities, over infinite fields.Namely, we decribe Z2-graded central polinomials for the algebras M2(K) (2 × 2 matrices over a field K), M1,1(E) (subalgebra of M2(E) whose entries on the diagonal belong to E0 and the off-diagonal entries lie in E1, E is the infinite-dimensional unitary Grassmann algebra, E0 is the center of E and E1 is the anticommutative part of E) and E ⊗ E. Also, we describe the central polinomials for e over a field K, with charK ≠ 2 and finally the central polinomial with involution for M2 (K), considering the transpose and the sympletic involutions.