Abstract: | Let A be an algebra over a field K of characteristic zero andlet 1, ..., sDer K(A) be commuting locally nilpotent K-derivationssuch that i(xj) equals ij, the Kronecker delta, for some elementsx1, ..., xsA. A set of generators for the algebra is found explicitly and a set of defining relationsfor the algebra A is described. Similarly, let 1, ..., s AutK(A)be commuting K-automorphisms of the algebra A is given suchthat the maps i – idA are locally nilpotent and i (xj)= xj + ij, for some elements x1, ..., xs A. A set of generatorsfor the algebra A: = {a A | 1(a) = ... = s(a) = a} is foundexplicitly and a set of defining relations for the algebra Ais described. In general, even for a finitely generated non-commutativealgebra A the algebras of invariants A and A are not finitelygenerated, not (left or right) Noetherian and a minimal numberof defining relations is infinite. However, for a finitely generatedcommutative algebra A the opposite is always true. The derivations(or automorphisms) just described appear often in many differentsituations (possibly) after localization of the algebra A. |