Abstract We study polynomial invariants of systems of vectors with respect to exceptional simple algebraic groups in their minimal linear representations. For each type we prove that the algebra of invariants is integral over the subalgebra of trace polynomials for a suitable algebraic system $\left( cf.\,[27],\,[28],\,[13] \right)$ .

Let (B, omega) be a Bernstein algebra over a field of zero characteristic and B = eF + U-e + Z(e) a Peirce decomposition. Regular algebras (that is Bernstein algebras in which U(e)Z(e) = Z(e)(2) = 0) and exclusive algebras (U-e(2) = 0) satisfying: U(e)Z(e) = 0 will be considered. Generators of the ideal of polynomial identities for these two classes of Bernstein algebras will be given. (C) 1998 Academic Press.

It is proved that Jordan pairs P(n, m) = (Mn, m, Mm, n) of n × m matrices over a field k are distinguished up to embedding by means of polynomial identities. Also, a basis of identities of P(1, n), where n can be infinite and the characteristic of k is equal to zero, is found.

Click to increase image sizeClick to decrease image size 1During 1993/94 a Becario de Ficyt at the University of Oviedo, Asturias, SPAIN Notes 1During 1993/94 a Becario de Ficyt at the University of Oviedo, Asturias, SPAIN